Low Reynolds Numbers in Practical Use

Low Reynolds Numbers in Practical Use
Miles Miller January 9, 2015

Examples of Low Reynolds Numbers in Practical Use
X-24A Lifting Body - External Flow Around Aircraft Liquid-Filled, Spinning Projectiles - Internal Flow in Spinning Cylinder Spinning Cylinder in Cross Flow - External Flow Around Spinning Cylinder Ring Airfoil Grenade - Small, Low-Speed Airfoil

Reynolds Number RL = V L/γ
Where: V = Velocity L = Reference Length γ = Specific Viscosity = (μ/ρ) μ = Viscosity ρ = Density

Martin X-24A Lifting Body

X-24A “Lifting Body” Experimental “Wingless” Space Plane
Lift generated from body shape alone (Lifting Body) Project ran from 1964 to 1967 Last “aircraft” designed and built by the Martin Company in Baltimore Youngest engineer on the project The X-24A was an experimental “Lifting Body” manned space plane. A “Lifting Body”, does not have wings like a conventional aircraft, but generate all of its lift from its body shape. The X-24A was the last “aircraft” designed and built by the Martin Company in Baltimore. Actually, Martin-Marietta Company - formed in 1965 (somehow aircraft and concrete didn’t seem to go together). All of the engineering work was done at the Baltimore (Middle River) facility. I was part of the Experimental Fluid Mechanics Section whose main efforts included wind tunnel testing. Martin did not have its own wind tunnels (except for the Hot Shot Tunnel), but went to NASA, Air Force, Navy and commercial facilities. I joined Martin right out of college. While I was educated as an Aerospace Engineer, the X-24A was the only ”aircraft” I worked on in my entire career. I worked on X-24A project from 1964 to 1967. I was the youngest engineer on the project. I helped in several wind tunnel tests on the X-24A and was the project Engineer for the B-52 Separation Tests which I will discuss later. Working on the X-24A was a very exciting experience for me.

X-24A First Powered Flight

For Hypersonic L/D Values
Landing Footprints For Hypersonic L/D Values Mercury Gemini Apollo (L/D = 0 to 0.3) Atlantic Ocean Pacific Ocean L/D =1.5 The vehicle flies in the hypersonic regime about 80% of the time from re-entry to landing. The hypersonic L/D is important for maneuvering during reentry. The higher the L/D , the greater the lateral range (cross-range) possible. For example, a hypersonic L/D of 1.5 represents a 1,500 mi. wide footprint. (All of western U.S.) Also, the ballistic footprint (red) is uncertain, whereas, the lifting footprint (green) is certain.

Stability and Control Over Multi-Speed Regimes
(Mach 25 to Mach 0.3) Re-entry (Thermal Protection) Mach Number = V/a a = 762 mph at sea level (t = 59o F) a = 658 mph above 36,000 ft. (t = -57oF) V = 17,000 mph (Space) V = to 3,400 mph Mach 25 to 5 (Hypersonic) Regime Mach Number Subsonic Transonic Supersonic Hypersonic V = 3,400 to 1,000 mph Mach 5 to 1.5 (Supersonic) V = 1,000 to 550 mph Mach 1.5 to 0.8 (Transonic) V = 550 to 200 mph Mach 0.8 to 0.3 (Subsonic) Landing (Glide Angle) . The vehicle had to be designed to fly in all speed regimes including Hypersonic, Supersonic, Transonic and Subsonic (Mach number 25 to 0.3). Each speed regime had its own aerodynamic configuration requirements to achieve the desired L/D and stability and control. Represents first manned vehicle to achieve this multi-flight regime capability. a = 1,118 S.L. a = 966 fps above 36,000 ft. (t = -57oF) Ve = 17,000 mph (25,000 fps) = Mach 25

Glide Angles for Subsonic Lift to Drag (L/D) Ratios
Lift (L) Glide Angle = tan-1 (D/L) Drag (D) Flight Direction Glide Angle Horizontal L/D Configuration Glide Angle Minimum for Safe Landing o Lifting Body o Space Shuttle o Cessna o Boeing 767* o U o Sport Glider o The subsonic L/D is important for landing. The greater the L/D, the shallower the glide angle and lower landing speed. The D/L ratio is equal to the amount of drop to the forward distance travelled. This chart puts this into perspective. Ranges from an L/D of 2.5 (minimum for a safe landing) To a high L/D of a sport glider (almost floats and is hard to get down). A lifting body just makes it! A major question of the lifting body program was: Could a low L/D vehicle be landed safely. Note: Boeing 767 has about the same L/D as a Cessna 172. Boeing 767 (Gimli Glider), 1983, Montreal to Edmonton, Canada, 40,000’, glided 84 miles, 250 mph, 20 min. Landed at Gimli, Canada * Gimli Glider” 1983, Air Canada Glided 84 miles from 40,000 ft. to landing.

Manned Lifting Body Flight Plan
Rocket Cut-Off Mach 2 100,000 80,000 60,000 40,000 20,000 Rocket Ignition (2.5 min.) Glide and Maneuver (5 min.) Altitude - Ft. Released from B-52 Mach 0.8 This illustrates the flight test sequence for all of the manned lifting bodies. This was intended to demonstrate the low speed (Mach 2 to Mach 0.3) flight characteristics including a gliding landing. Lifting bodies were dropped from B-52 at 45,000 ft. altitude and Mach 0.8. Initial tests were unpowered, gliding flights. For powered flights, rocket ignited for 2.5 min. boost to Mach 2 and a 100,000 ft. altitude. Rocket cut-off and vehicle glides for 5 min. to landing at Mach 0.3 (220 mph). Glide and Maneuver (3 min.) Horizontal Landing Mach 0.3 .

Reynolds Number Velocity and Length Upper and Lower Rudders
X-24A Reynolds Number Velocity and Length RL = V L/γ Where: V∞ = Free Stream Velocity L = Reference Length γ = Specific Viscosity = (μ/ρ) μ = Viscosity ρ = Density Out Fins Center Fin 11.5 ft. Upper and Lower Rudders 24.5 ft. Upper and Lower Flaps 9.6 ft. V∞ L = 23 ft. Empty weight: 6,360 lb Loaded weight: 10,700 lb Sta. 0.0 Sta

Wind Tunnel vs. Flight Test
Tunnel wall Aerodynamic effects are identical (except for model scale and Reynolds number effects) Scaled Aerodynamic Effects Aerodynamic Effects Air Flow Flight Direction Mount Stationary Model, Moving Air Moving Aircraft, Stationary Air Tunnel wall Advantages of Wind Tunnel Less expensive - Use of scale model Safer - Don’t have to build and fly untested aircraft Parametric studies - Easy configuration changes Precise measurements - Sensitive instrumentation Wind tunnels designed for different Mach numbers

X-24A in University of Maryland,
Continuous Flow, Low Speed Wind Tunnel 150 mph (Mach 0.2) 20% Scale, Wooden Model Air Flow Tufts External Force and Moment Balance The SV-5P design was evolved through testing in several different wind tunnels. All of the subsonic wind tunnel tests were performed in the University of Maryland 8 X 11-Ft. Subsonic Wind Tunnel. This is a continuous flow tunnel with the aerodynamic forces and moments were measured by a balance located beneath the floor. A 20% scale wooden model was used in these tests. Tests conducted at Mach 0.2 (150 mph). Fabric tufts indicate local airflow patterns. Martin had the Hot Shot Tunnel in Baltimore, but all other wind tunnel tests were performed elsewhere. University of Maryland, NASA-Langley (8’ TPT, 7X10’ HST, Unitary Tunnels), NASA-Ames, Cornell, Princeton, Arnold (AETC) and North American (7X7‘ TWT). I had helped out on several of these tests: Subsonic force and moment test in U. of MD wind tunnel Transonic force test in NASA-Langley 8-ft. Wind tunnel Supersonic force and moment test in North American Trisonic Wind Tunnel Supersonic and dynamic stability tests in NASA Langley Unitary wind tunnel.

X-24A Model in North American 7x7-Ft. Blow-Down, Trisonic Wind Tunnel
(Mach 0.5 – 1.2) 8% Scale, Steel Model Internal Force and Moment Balance Sting Mount I was part of the team that tested the SV-5P at the North American Aviation, 7 X 7 - Ft. Trisonic Wind Tunnel in Los Angeles, CA. Located adjacent to the Los Angeles International Airport, the tunnel was a blow-down type whose Mach number was set by means of a 2-dimension, flexible nozzle. The contour of the 1-inch steel, nozzles were adjusted and held in place by hydraulic jacks. Tunnel was capable of operating in the subsonic, transonic and supersonic speed regimes. Large air tanks upstream were filled with high pressure air and released into the tunnel nozzle inlet. The air exhausted into vacuum tanks down stream of the tunnel test section. As with all blow-down tunnels, the initial transient flow produced loads on the model that were quite severe about 3 times the steady state loads. The SV-5P model experienced a normal force over 2.5 times the NAA estimated maximum “starting load” at Mach 2.2. ***While setting up for the test, we noticed large gouges in the sides of the tunnel downstream of the test section. We were told that these were caused by the Douglas CX-HLS (entry for what became the C-5) wind tunnel model as it was blown down the tunnel after it broke loose from its sting mount during recent tests. I later found out that the lack of transonic wind tunnel data due to this accident was one reason for Douglas not winning the C-5 contract. ***When the tunnel was operated, the noise and vibration were overwhelming. During model changes, we were huddled around the model in the test section which was extremely cold due to the expanding air. While the air tanks were being pumped up. occasionally a relief valve would pop release a loud hissing noise. This occurred randomly and every time this happened, we thought the main tunnel valve had opened and the tunnel was operating . It was very nerve wracking!

X-24A Mounted to B-52 X-24A Pylon Adapter X-15 Pylon
This is a close-up of the X-24A mounted to the B-52.

X-24A/Pylon Adapter and B-52 Models
NASA Langley, 7 x 10- Ft. High Speed Wind Tunnel (Mach 0.6 – 0.85) 2.5% scale X-24A and pylon adapter models attached to B-52 model in the 7 x 10-Ft. NASA-Langley High Speed wind tunnel. Wind tunnel tests were performed at the NASA-Langley 7x10-Ft. High Speed Wind Tunnel in the spring and summer of 1966 (to evaluate a modified pylon adapter). The tunnel was continuous flow, tunnel with a top speed of Mach 0.85. Air flow produced by an 18 blade propeller powered by a 35,000 hp electric motor. The test section where the model was located was 7 feet high and 10 feet wide. The same 2.5% scale model of the B-52 was used that had been used for the X-15, M-2 and HL-10 separation tests. A 2.5% scale B-52 model was the largest size that would be compatible with the tunnel test section size. 2.5% Scale Models

Computer Separation Motion Based on Wind Tunnel Data
5 10 15 t = 0 sec. t = 0.2 sec. t = 0.4 sec. t = 0.6 sec. Distance Dropped – ft. t = 0.8 sec. The data obtained in the wind tunnel test were then used in computer program to calculate the motion of the SV-5P after it was released from the B-52. Simulated drops under a variety of launch conditions (B-52 velocity and altitude) and different SV-5P attachment conditions. Drops were simulated with no pilot import and also with control surface movements to represent pilot input (termed motion dampers). This figure shows the SV-5 body location and attitude at 0.20 sec increments. Note the characteristic roll motion initially to the left and then to the right created by the air flow over the B-52 wing and pylon. For this case, vehicle yaws to the right throughout drop, yet its initial rolling motion is to the left (opposite of free stream case) until it clears B-52 flow field where it rolls to the right. The SV-5P initially experiences a slight negative roll at all Mach numbers. While the general motion predicted by the wind tunnel tests were correct, the actual flight motions were not as pronounced. At the lower Mach numbers, vehicle initially rolls left and at the higher Mach numbers, it initially rolls right. Simulated drops were made with and without autopilot motion dampers (representing pilot input). Based on normal acceleration and clearance considerations, a “carry angle “ of +1.5 deg. was selected. Maximum vertical load on pylon was when B-52 was taxiing and passing over joints in concrete runway. Lateral loads larger than expected. Wind tunnel test, data plotting and motion analysis took several months. M = 0.8 Altitude = 44,000 ft. αB-52 = -2o X-24A Weight = 6,280 lbs. Carry angle = 2.5o Dampers Operating No Pilot Action t = 1.0 sec.

Effect of Launch Mach Number on X-24A Yawing and Rolling Motion
ψ Mach 0.8 Mach 0.6 Altitude: 44,000 ft. X-24A Weight = 6,280 lbs. No Pilot Action Roll Angle (φ) - Deg Yaw Angle (ψ) - Deg. Top View φ Mach 0.8 Wind tunnel data revealed dramatic effect of B-52 flow field on X-24A roll motion. At Mach 0.6, it rolls left and at Mach 0.8, it rolls right. This rolling motion is due to X-24A yawing motion produced bhy he B-52 flow field. A yaw to the right results in a roll to the left and a yaw to the left produces a roll to right. B-52 angle-of-attack is +2 deg. at Mach 0.6 and -2 deg. at Mach 0.8. At 44,000 ft. a = 662 mph – Mach 0.6 to Mach 0.8 = 132 mph difference in speed. Mach 0.6 Pilot View Time - Sec. Distance Dropped ft ft ft ft ft ft.

Comparison of Flight vs. Simulation
X-24A/B-52 Separation Speed = Mach 0.65 Altitude: 44,000 ft. X-24A Weight = 6,280 lbs. Flight (Re = 43, ) Simulation (Re = 1,800,000) Roll Angle – Deg Yaw Angle – Deg Pitch Angle – Deg. This chart compares the flight motion of the X-24A during the first 2 seconds after release from the B-52 at Mach 0.65. Flight data are compared to simulation results. Simulation data are from the Martin Separation Wind tunnel report and were generated using wind tunnel data and a very basic flight motion program. Note that the trends are similar, but the flight motion is not as severe as predicted by the simulation. Better this way than to underestimate the severity of the motion. Time – Sec. Distance Dropped ft ft ft.

Actual X-24A Vehicle in NASA-AMES 40 x 80-Ft. Full Scale Wind Tunnel
One of the advantages of a wind tunnel is that you don’t have to test the actual, full scale aircraft. It is rare that a full scale vehicle can be tested in a wind tunnel and the data compared with subsequent flight results. Prior to flight tests, the actual SV-5P was tested in the NASA Ames full scale wind tunnel. The mounting legs are attached to a force and moment balance underneath the wind tunnel. The vehicle was tested with landing gear extended and retracted. Tests with simulated post-flight, rough ablative surface revealed a 30% loss of L/D!

Lift and Drag Coefficients
Pitching Moment Pointing Direction Angle-of-Attack (α) V Drag Flight Direction Lift = Shape (CL) X Air Density (ρ) X Velocity Squared (V2) X Size (S) Lift = CL x ρV2 x S 2 Drag = CD x ρV2 x S Drag = Shape (CD) X Air Density (ρ) X Velocity Squared (V2) X Size (S) Two of the major factors in a projectile’s flight performance are the Lift force and Drag force. These forces are a function the shape, angle-of-attack, air density, velocity and size. The size is represented by a reference area associated with the projectile, usually the projected frontal area. The lift and drag coefficients are non-dimensional terms that represent the shape of the projectile. The plot of the coefficients against the angle-of-attack indicates the basic flight behavior of the shape. When multiplied by the density, velocity squared and area, it gives the forces in lbs. Often the coefficient is a function of the Mach number (velocity in terms of the speed of sound) and the Reynolds number (when the air viscosity, velocity and size are extreme) Pitching Moment = Shape (Cm) X Air Density (ρ) X Velocity Squared (V2) X Size (S) X Length (L) Pitching Moment = Cm x ρV2 x S x L 2 CD and CD are only a function of: Shape Angle-of-Attack (α) Mach Number Reynolds Number (Velocity, Length, Viscosity) CL, and CD, and Cm are not a function of: Velocity Air density Size

SV-5P Wind Tunnel Model Scales and Reynolds Numbers (Landing Speed)
Flight 2.5% Scale Model Mach Re = 2,000,000 8% Scale Model Mach Re = 7,000,000 100% Scale (Actual Aircraft) Mach 0.3 Re = 50,000,000 20% Scale Model Mach 0.2 Re = 7,000,000 100% Scale (Actual Aircraft) Mach 0.2 Re = 30,000,000

X-24A Subsonic Lift Coefficient Data from
Wind Tunnel Tests With Various Scale Models Mach = 0.65 0.6 0.5 CL 0.4 α Direction Flight Lift Coefficient (CL) 0.3 2.5% 8% 20% 100% Flight Test Sym. Scale CL not a function of: Velocity Air density Size CL only function of: Shape 0.2 As noted, the SV-5P was wind tunnel tested in various scales (2.5, 8, 20 and 100%). The question may be asked as to how accurate are the data from the different scale models, especially the 2.5% scale model used in the B-52 drop test. Scale mandated by the B-52 model size. This chart compares the lift coefficient with angle-of-attack for the four wind tunnel test model scales and full scale flight test results. The lift coefficient is a term that is only based on the shape of the item tested. It is independent of size, air density and air speed (except for Mach number). The larger scale models can have more detailed features. 0.1 2 4 6 8 10 12 14 16 Angle of Attack (α) – deg.

X-24A Subsonic Drag Coefficient Data from
Wind Tunnel Tests With Various Scale Models Sym. Scale 2.5% 8% α 20% CD not a function of: Velocity Air density Size CD only function of: Shape 100% Flight Test These data compare the drag coefficients vs. angle-of-attack. Note, again, the excellent agreement of the different model scale tests. 0.1 18

Pitching Moment Coefficient vs. Angle of Attack
Martin SV-5P/X-24A Pitching Moment Coefficient vs. Angle of Attack Cm

The rolling moment coefficient was particularly important for the B-52 separation tests.
This plot shows the Rolling Moment due to a combination of sideslip and angle-of-attack. Negative coefficient means that the vehicle rolls away from the apparent wind direction. The rolling moment coefficient vs. angle-of-attack also shows good agreement between the various scales tested. Certainly good enough for the purposes of the separation test. The lifting body program illustrated the need to interpret the wind tunnel data correctly. Flight problems were indicated in the wind tunnel data, but often discounted or ignored.

Mach = 0.65 β CY The side moment derivative wrt sideslip angle is presented here and shows good agreement with no discernable trends with model scale.

β Cn The yawing moment derivative wrt sideslip angle is presented here and shows good agreement. Top View

Liquid-filled Projectiles

Liquid-Filled Projectile Reynolds Number Velocity and Length
Rd = V d/γ Rd = ω d2/2γ Where: V = Cylinder Interior Tip Speed = ωd/2 ω = Cylinder Spin Rate d = Cylinder Inside Diameter γ = Specific Viscosity = (μ/ρ) μ = Viscosity ρ = liquid density ω Payload Canister (Liquid-Filled Cylinder) 155 mm Artillery Projectile d

Spin Stabilized Projectile Motion Nutation - Fast Frequency (ωN) Only
Combined Nutation - Fast Frequency (ωN) and Precession -Slow Frequency (ωP) Nutation - Fast Frequency (ωN) Only Epicyclic Motion Coning Motion Plane to Velocity Vector Plane to Velocity Vector V V θ p θ p ωN and ωP ≈ Cmα For Spin Stabilized Projectile: ωN/ωP ≈ 11

Coning (Nutation) Frequency (ωN)
Coning Motion θ = θ0 eλt λ = (1 + τ) τ Mq (Mpa + ML) 2I Ix Spin Rate (p) Where: θ = Coning (Nutation) Angle λ = Aerodynamic Terms Mq = Aerodynamic Damping Moment Mpα = Magnus Moment ML = Liquid-Fill Moment τ = 1/Sg p2Ix2 Sg = 4IMα Mα = Aerodynamic Pitching Moment Note: Ix = I/10 Velocity (V) Coning Angle (θ) Spin Axis Coning (Nutation) Frequency (ωN) Flight Direction When a projectile exits the gun tube, it is followed by the high pressure gases from the propellant charge. This gas flow interacts with the projectile and “kicks’” it to a large yaw angle (angle between the direction it is flying and the direction it is pointing. This angle is termed the “first maximum yaw”. Because the projectile is spinning, it assumes “coning” motion where the spin axis motion generates a conical surface with the yaw angle as its apex angle. A stable projectile will fly on with a decreasing yaw angle, whereas for an unstable projectile, the yaw angle will increase eventually causing the projectile to fall short range. Spin Axis Spin Rate (p)

Types of Flight Stability
θ - deg. θ - deg. θ - deg. t – sec. t – sec. t – sec. Unstable Stable Neutrally Stable

Effect of Liquid Viscosity on Resonance Type Liquid-Fill Instability

Resonance Type Instability
Existing Theory (Liquid Resonance Destabilizing Moment) Destabilizing Moment Destabilizing Moment with Increasing Viscosity (Decreasing Reynolds Number) Instability Decreases 100 102 104 106 Increasing Viscosity Decreasing Reynolds Number 100 Viscosity - cSt Increasing Coning Rate/spin Rate 102 Reynolds Number (ωd2/γ) 104 106

Initial Test Fixture for Non-Rigid Payloads Film
M Old Spin Fixture.wmv. (1 min. 45 sec.): This film depicts the initial version of the spin fixture that was used to determine the source of the XM761 flight problem as well as discovering the high viscosity fill instability.

Effect of Viscous Liquid-Fills on Projectile Instability
* Despin moment normalized by liquid density Corn Syrup (Pancake Syrup) θ = 20 deg. Ω = 500 rpm ω = 6,000 rpm ML Payload Induced Destabilizing Moment* (ML) – ft.-lbs. l = 20.36” Glycerol (Anti-Freeze) d= 4.75” l/d = 4.3 Propylene Glycol (Mineral Oil) The XM761 canister was tested on the Spin Fixture with an array of viscous liquids including water, propylene glycol (baby oil), glycerin, and corn syrup (pancake syrup) at various temperatures to obtain viscosities from 1 through 1,000,000 CS. The measured destabilizing moment for the transonic (Zone 4) launch conditions are shown here plotted against the liquid viscosity. The unit of viscosity is centi-stokes which may not be familiar. So I have out in the more familiar items having the same range of viscosity. The viscosities of glycerol and corn syrup are very dependent on their temperatures. The viscosities used in the tests were achieved by pre-cooling the liquids to known temperatures and relating their respective viscosities to these temperatures. The smooth curves were obtained by ratioing the measured moments by their respective liquid masses. Note how the instability (shown by the spin rate moment) increases from a viscosity of 1 and peaks out a 100, 000 CS (pancake syrup) and then decreases. This was the first ever measurement of this effect. Note also, that the maximum moment for the viscous liquid fill is equal to that of the original XM761 payload. The large quantity of corn syrup used in the tests was provided by King Syrup Company of Baltimore. It is the main ingredient used to manufacture King Pancake Syrup. They did not know the viscosity of the corn syrup and used the simple falling sphere Stokes Flow measuring apparatus as a Go/No-Go quality control test during pancake syrup manufacturing. Water Viscosity -Centi-Stokes Reynolds Number (Rd)

Flight Motion of Artillery Projectile
with Corn Syrup (High Viscosity) Liquid-Fill Coning Angle -deg. Time - sec. This plot illustrates the similarity between an unstable flight of the XM761 and an unstable flight of the same projectile having a viscous liquid fill. Note the similarity in the increase in yaw angle and simultaneous decrease in spin rate. Spin Rate - rps Time - sec.

3-D Plot of Viscous Liquid-Fill Destabilizing Moment
New Phenomenon - Viscous Liquid Destabilizing Moment Destabilizing Moment Cylinder Aspect ratio (l/d) = 4.5 .10 Increasing Coning Motion 108 .3 Increasing Viscosity 106 .05 1010 100 102 104 106 108 Decreasing Reynolds Number 104 .2 102 Viscosity - cSt Coning Rate/Spin Rate 100 .1 Reynolds Number (ωd2/γ) 10-2 10-4

3-D Plot of Combined Resonance
and Viscous Liquid Destabilizing Moments Existing Theory for Low Viscosity Liquids Destabilizing Moment Caused by Liquid Resonance Dependent on Aspect Ratio of Container , Ratio of Spin to Coning Rate and Fill Level New Phenomenon for Viscous Liquids Destabilizing Moment Caused by Liquid Velocity Field Not Dependent on Aspect Ratio of Container, Ratio of Spin to Coning Rate or Fill Level Destabilizing Moment .10 .05 .10 100 102 104 106 .3 ..05 .2 Increasing Coning Rate/spin Rate .1 Increasing Viscosity Decreasing Reynolds Number Cylinder Aspect Ratio (l/d) = 4.5

Two Types of Liquid-Fill Destabilizing Causes
Existing Theory for Low Viscosity Liquids Destabilizing Moment Caused by Liquid Resonance Dependent on Aspect Ratio of Container , Ratio of Spin to Coning Rate and Fill Level New Phenomenon for Viscous Liquids Destabilizing Moment Caused by Liquid Velocity Field Not Dependent on Aspect Ratio of Container, Ratio of Spin to Coning Rate or Fill Level Destabilizing Moment ..05 .10 .10 Prior to this discovery, the theory for liquid filled projectiles first developed indicated a sharp moment at a very narrow and specific motion condition (coning rate to spin rate ratio) and decreases with increasing viscosity (shown in green). This was created by the a liquid resonance phenomenon and is termed a “Resonance” type instability. Note, how the destabilizing moment is decreasing with increased viscosity which was predicted by the existing theories as the more viscous liquid would “dampen out” any pressure waves in the spinning fluid. A “Viscous” type instability increases with increasing viscosity and then decreases at very high viscosities (shown in red). Based on the Edgewood experimental data, Herbert evolved a “Unified” theory that would apply over the entire range of liquid viscosities. Note, how the new instability increases with viscosity to a peak value and then abruptly decreases which agrees with the Edgewood data. .3 106 ..05 .2 104 Increasing Viscosity Increasing Coning Motion .1 102 100

3-D Plot of Liquid-Fill Destabilizing Moment
Coning Rate (ω) Spin Rate (p) Coning Angle (θ) Despin Moment (ML) Despin Moment Canister Aspect Ratio = 4.5 .10 .05 ..05 .10 Inside Diameter (d) Coning Rate /Spin Rate (ω/p) Prior to this discovery, the theory for liquid filled projectiles first developed indicated a sharp moment at a very narrow and specific motion condition (coning rate to spin rate ratio) and decreases with increasing viscosity (shown in green). This was created by the a liquid resonance phenomenon and is termed a “Resonance” type instability. Note, how the destabilizing moment is decreasing with increased viscosity which was predicted by the existing theories as the more viscous liquid would “dampen out” any pressure waves in the spinning fluid. A “Viscous” type instability increases with increasing viscosity and then decreases at very high viscosities (shown in red). Based on the Edgewood experimental data, Herbert evolved a “Unified” theory that would apply over the entire range of liquid viscosities. Note, how the new instability increases with viscosity to a peak value and then abruptly decreases which agrees with the Edgewood data. Resonance Type Instability Reynolds Number (Rd= ωd2/γ) Viscous Type Instability Despin Moment 0.0 Reynolds Number (Rd)

Relation of Viscous Liquid-Fill Yaw and Despin Moments
θ Yaw Despin Yaw Despin Despin Moment Tan θ Yaw Moment = Spin Rare = 6,000 rpm Coning Rate = 500 rpm Canister Aspect Ratio = 4.5 Viscosity = 80,000 cSt

3-D Liquid-Fill Instability Plot Computed by “Unified Theory”
Destabilizing Moment Caused by Liquid Resonance Destabilizing Moment Caused by Viscous Liquid “Unified Theory” Can Predict Destabilizing Effect for Both Resonance and Viscous Instabilities Initial Spin Fixture Experiments Destabilizing Moment All canister aspect ratios All liquid fill densities All liquid fill viscosities All projectile flight motions The “Unified” theory computes the 3-D plot for any liquid fill and projectile motion case. Coning Rate /Spin Rate Projectile Motion Reynolds Number Liquid Fill Properties

Types of Flight Stability
γ = 1,000 cSt Rd = 3,900 γ = 6,700 cSt Rd = 300 γ = 100,000 cSt Rd = 26 θ - deg. θ - deg. θ - deg. t – sec. t – sec. t – sec. Unstable Stable Neutrally Stable

Void Shape In Spinning and Coning Liquid filled Cylinder
Canister Length/Diameter = 4.3 Viscosity = 1,000 cSt Coning Rate /Spin Rate = 0.167 Coning Angle = 20 deg. Initial studies on the Edgewood Spin Fixture obtained photos of the air void shape in the spinning and coning canister. Spark photography was used to observe the instantaneous shape of the 10% void of the simultaneously spinning and coning liquid-filled transparent canister. The sinusoidal shape provided insight into the internal flow and were very helpful in evolving and validating the theories as depicted by the computed results on the right. Remarkably, the void shape remains in the same plane as the coning angle. Experiment CFD Computation

Computed Internal Flow Field
In Spinning and Coning Liquid filled Cylinder Computational Fluid Dynamics (CFD) approaches were employed to compute the internal flow and the resulting pressures and moments. Color coding was used to illustrate the various types of flow and velocity profiles that create the void shape. Velocity and Pressure Pressure

Spinning Projectile Flight Instability Sources
Magnus Instability: (Externally Produced Yawing Moment) Resonance Type Liquid-Fill Instability: (Internally Produced Yawing Moment) XM761 Instability: (Internally Produced Yawing and Despin Moment) Other known types of spinning projectile flight instabilities did not affect the spin rate. The despin phenomenon was the new feature and would seem to be an integral element of the instability.

Effect of Reducing Canister Length
on Resonance Type Liquid-Fill Instability Aspect Ratio = 3.325 Diameter = 5 in. Length = in. Reduction in length Change in length = in. Aspect Ratio = 3.176 Diameter = 5 in. Length = in.

Effect of Fill level for Low and High Viscosity Liquid Fills
on Destabilizing Moment Aspect Ratio = 4.5 Spin Rate = 6,000 rpm Coning Rate = 500 rpm Coning Angle = 20 deg. 1 cSt (Water) 100,000 cSt (Pancake Syrup) 3 2 1 Fill Level - % Destabilizing Moment - ft.-lbs.

Low Viscosity, Immiscible Liquid Additive
to Reduce Viscous Liquid Payload Induced Flight Instability Projectile Body Spin High Viscosity Liquid Payload Projectile Cross Section Higher density, low viscosity, immiscible liquid additive centrifuged out to form a thin layer between lower density, high viscosity liquid payload and inner wall of projectile body Low Viscosity, Immiscible Liquid Additive

Effect of Immiscible, Low Viscosity Additive
in Reducing Destabilizing Moment of Highly Viscous Liquid-Fill 3 2 1 Amount Viscosity Density Payload % ,000 cSt gm/cm3 Additive % cSt gm/cm3 Coning Angle = 20 deg. Coning Rate = 500 rpm Flight Spin Rate Destabilizing Moment - ft.-lbs. Without Additive Reduction in Destabilizing Moment This shows the reduction in the despin moment (proportional to the destabilizing yawing moment) when 2% of a 1 cS (water) additive is added to the 100,000 cS payload. The projectile would not be stable with the 100, 000 cS fill, but would be stable with the additive. With Additive , , , ,000 Spin Rate - rpm

Flight Test Demonstrating Effect of Immiscible, Low Viscosity Additive in Reducing Destabilizing Moment 10,000 cS 10,000 cS with Additve Coning Angle - deg. Coning Angle - deg. Spin Rate - rps Spin Rate - rps Time - sec. Time - sec.

Viscous Liquid Type Flight Instability Summary
Spin Fixture data reveals large liquid-induced flight instability due to highly viscous liquid fills - verified via flight tests Parametric studies on spin fixture characterize instability properties: - Measurement of associated liquid-induced yaw moment - Instability not sensitive to aspect ratio - Instability not sensitive to fill ratio - Instability not sensitive to surface roughness - Instability reduced for Non-Newtonian (shear thinning) liquid fills Theoretical (mathematical) model of viscous liquid instability evolved and validated via spin fixture data Unified Theory developed to predict flight instabilities for any liquid payload at any flight condition Instability reduced by small amount of Immiscible, low viscosity liquid

Magnus: Spinning Cylinder in Cross Flow

Flow Field, Surface Pressures, Forces
This pressure distribution represented the important middle stage between the flow field and the resulting forces acting on the body. The high spin rate of the body precluded the standard pressure measuring technique of placing static pressure taps on the surface and the resulting centrifugal loads and rapid pressure changes over the circumference of the model ruled out placing pressure transducers in the model surface.

Cylinder in Cross-Flow Reynolds Number Velocity and Length
RD = V d/γ Where: V = Free Stream Velocity d = Cylinder Outside Diameter γ = Specific Viscosity = (μ/ρ) μ = Viscosity ρ = liquid density d V∞ The 5.2 in. diameter and 8.5 in. span cylindrical model was constructed of aluminum and mounted with its spin axis oriented vertically in the Edgewood 40 X 28 - In. Subsonic Wind Tunnel. The model included 9.3 in. diameter, circular end plates to eliminate edge flow effects and provide the two-dimensional flow over a spinning cylinder desired. Model spin was provided by means of an electric motor located above the tunnel test section and connected to the model by a vertical drive shaft. The model was attached to the tunnel turntable below by a central strut through which a pressure tube could be routed to instrumentation located outside of the wind tunnel. The pressure tap located in the core was forced against the inner surface of the spinning shell by means of four small coil springs. Lubrication grease was applied to the inner surface of the shell by a remotely operated grease gun mechanism for sealing and reduced friction.

v∞ Surface Pressures on Non-Spinning Cylinder in Cross-flow
for Sub-Critical, Critical and Super-Critical Reynolds Numbers Potential (Invisid) Theory Super-Critical Sub-Critical CP v∞

Sub-Critical, Critical and Super-Critical Conditions for Cylinder
The flow over a non-spinning, circular cylinder in cross-flow produces three distinct flow conditions depending on the Reynolds number. These relate to the transition of the boundary layer on the surface of the cylinder from totally laminar at the lower Reynolds numbers to totally turbulent at the higher Reynolds numbers. The corresponding drag acting on the cylinder undergoes an abrupt change from a high to a low value for these respective cases. The high drag condition is termed “sub-critical”; the low drag condition is termed “super-critical”; and the Reynolds number at which the drag value is half way between these extremes is termed the “Critical” Reynolds number. Wind tunnel tests were initially performed with the non-spinning cylinder model to determine the critical Reynolds number conditions for the model in the Edgewood wind tunnel.

Method to Measure Surface Pressures on Spinning Body
A new and unique experimental approach was evolved by the WSCO to obtain these measurements. A two-part model was employed having a stationary inner core containing a single pressure tap and the spinning outer shell representing the spinning surface of the body. The outer shell included a single vent hole that aligned with the pressure tap once every revolution of the shell. The gap between the moving outer surface and the stationary inner surface was sealed by means of a sliding "o" ring located in the core.

Surface Pressure Cylinder Model in Wind Tunnel Right Circular Cylinder
Spin Motor Drive Shaft End Plates Right Circular Cylinder Balance Strut The 5.2 in. diameter and 8.5 in. span cylindrical model was constructed of aluminum and mounted with its spin axis oriented vertically in the Edgewood 40 X 28 - In. Subsonic Wind Tunnel. The model included 9.3 in. diameter, circular end plates to eliminate edge flow effects and provide the two-dimensional flow over a spinning cylinder desired. Model spin was provided by means of an electric motor located above the tunnel test section and connected to the model by a vertical drive shaft. The model was attached to the tunnel turntable below by a central strut through which a pressure tube could be routed to instrumentation located outside of the wind tunnel. The pressure tap located in the core was forced against the inner surface of the spinning shell by means of four small coil springs. Lubrication grease was applied to the inner surface of the shell by a remotely operated grease gun mechanism for sealing and reduced friction.

Surface Pressure on Spinning Cylinder
The measured pressure data were integrated over the surface of the model to obtain the lift and drag coefficients. These integrated pressure values were compared with the directly measured force data with excellent agreement achieved. This project demonstrated the experimental technique for a spinning model with a smooth external surface under steady flow conditions and represented the first time that validated surface pressures had ever been experimentally obtained on any spinning wind tunnel model.

Surface Pressures on Spinning Cylinder in Cross flow

Circumferential Surface Pressure Distribution on Boattail
(4 deg. and 10 deg. Angles-of-Attack) Angle-of-Attack (α) V Boattail Location The circumferential pressure distribution clearly showed the large negative pressure on the retreating side of the body and a positive pressure on the advancing side, both of which contributed to the Magnus force. This effect was accentuated at a 10 deg. angle-of-attack with two pronounced humps. A smaller hump on the advancing side was evidently due to a separation line on the upper leeward surface or a small shed vortex acting along the body. This latter phenomenon had never been detected before. Effect of Shock Wave on Advancing side

Magnus Side Force Distribution and Summation
on Spinning Artillery Projectile Sym Data Source α- deg. CFD BRL Experimental BRL Experimental Edgewood CFD BRL Experimental BRL Experimental Edgewood Correct Values in Color Symbol: Closed Open Type Data: Force Pressure Tunnel: Cornell 8-ft NASA Ames 14-ft. Model diameter: in in. Model Reynolds number: , ,650,000

Base Pressure Measurements on Spinning Artillery Projectile
Symbol: x Open Closed Type Data: Wind Tunnel Wind Tunnel Flight Tunnel: Sandia 1-ft NASA Ames 14-ft Model Diameter: in in in. Reynolds number: , ,650, ,000,000

Ring Airfoil Grenade (RAG A)
This session will describe projects associated with spinning, ring shaped projectiles where the cross section is an airfoil.

Airfoil to Ring Airfoil
The RAG consisted of a relatively thick airfoil in the form of a ring. The spin stabilized, shape produced a lift force which allowed to achieve long ranges while being fired at a relatively low elevation angle.

Ring Airfoil

Ring Airfoil Grenade (RAG)
Flat Trajectory The Ring Airfoil Grenade (RAG) was conceived by Abe Flatau in the mid 1960's. Inspiration for the device came about by problems encountered by the U. S Army in Vietnam where the enemy could be seen, but could not be engaged by the 40mm grenade launcher because its high arcing trajectory caused it to impact the foliage above the enemy position. What was needed to overcome this situation was a grenade that possessed a relatively flat trajectory in order to fly beneath the foliage canopy. While this could be achieved with a high velocity round, the weight of a grenade would produce prohibitively high recoil for a shoulder fired application. The RAG, while having a low muzzle velocity and low recoil, possessed a flat trajectory due to its aerodynamic properties. 40mm Grenade Arcing Trajectory

Muzzle Exit In Flight How Does Ring Airfoil Fly? ̰ Lift = Weight α
High gyroscopic stability keeps RAG pointing at a fixed angle to the ground ̰ Lift = Weight Direction RAG is Pointing Spin α Direction RAG is Flying Velocity Flight Path Spin Flight path curvature due to gravity automatically creates angle-of-attack and lift Velocity α = 0 Weight This illustrates how the RAG has such unusual flight characteristics. The RAG is launched at a relatively low angle of elevation relative to the ground (2-8 deg.). At launch, the RAG is pointing in the same direction as it is flying. Therefore, the angle-of-attack is zero as is the lift. As the RAG flies, its drag reduces its velocity and gravity causes it to fly at a lower angle to the ground than it was launched at. However, the high gyroscopic stability of the RAG keeps it pointing in the same direction as it was launched. This creates an angle-of attack between the direction it is pointing and the direction it is flying. Consequently, a lift force is generated due to the angle-of-attack and the resulting lift counteracts the gravity effect keeping the RAG flying at a shallow angle relative to the ground. Lift is generated automatically as the RAG flies creating just enough lift to keep it from falling. Weight Muzzle Exit In Flight

Typical Trajectories for
40mm M406 and 64mm RAG This shows a typical trajectory for the 64mm RAG and the standard M406 40mm grenade and illustrates how flat trajectory of the RAG.

Original “Notched Wire” RAG
Pre-coined fragmenting steel body Relatively Thick Airfoil Shape A RAG diameter of 2.5 inches (64mm) was selected to avoid any orifice flow through the hole that would increase the drag. It was fabricated from a “notched wire” (pre-coined) steel body that included an arbitrary thick airfoil to contain an explosive fill. Before any aerodynamic studies were undertaken, the basic RAG shape was fabricated into a coined configuration which was filled with a high explosive and tested in an explosive arena to evaluate its terminal effects. These tests showed it to have excellent fragment velocities and spray patterns.

Reynolds Number Velocity and Length
Ring Airfoil Reynolds Number Velocity and Length RL = V d/γ Where: V = Free Stream Velocity d = Maximum Outside Diameter γ = Specific Viscosity = (μ/ρ) μ = Viscosity ρ = liquid density d V∞ A 2.5 in. diameter RAG with this airfoil was fabricated from aluminum and tested in the Edgewood 34 X 24 - In. Subsonic Wind Tunnel. These tests showed this RAG configuration to have an excellent lift slope and low drag up to a stall angle of 20 deg. Also, the position of the center-of-pressure of the RAG experienced very little movement with angle-of-attack.

Full Scale RAG Model Installed in Wind Tunnel Model
Lift Force Full Scale, Aluminum Wind Tunnel Model Air Flow Drag Force Support Strut to Force Measuring Device Wind Shield A 2.5 in. diameter RAG with this airfoil was fabricated from aluminum and tested in the Edgewood 34 X 24 - In. Subsonic Wind Tunnel. These tests showed this RAG configuration to have an excellent lift slope and low drag up to a stall angle of 20 deg. Also, the position of the center-of-pressure of the RAG experienced very little movement with angle-of-attack.

Full Scale Notched Wire RAG Wind Tunnel Model
The actual RAG explosive test article was then tested in the Edgewood wind tunnel to evaluate its aerodynamic performance. It was mounted on a strut and tested at various yaw angles (angles-of-attack) with lift, drag and pitching moment measured at different air speeds.

Original RAG Aerodynamic Characteristics
Velocity = 220 ft./sec. Reynolds number = 328,723 0.6 0.4 0.2 -0.2 Lift Coefficient (CL) Drag Coefficient (CD) Direction of Flight α Spin Axis CL Pitching Moment (Cm) V 0.4 0.2 CD The airfoil was made exceptionally thick in order to contain as much explosive as possible - approaching a 30% thickness to chord ratio. Again, this is extremely large compared to most aircraft wing thicknesses of around 10% - 15%. This shows the lift, drag and pitching moment coefficients for the original RAG airfoil shape at a typical flight velocity. The green lines indicate what satisfactory data should look like. Note the low, erratic and non-linear lift, the high drag and large pitching moment - all undesirable. Designing an airfoil to operate at the small size an slow velocity of the RAG is not simple, especially if it is a relatively thick airfoil. The Reynolds numbers corresponding to these low velocities and small projectile are several orders of magnitude smaller than for a typical airplane and for any available airfoil data. 0.10 0.05 -0.05 -0.10 Cm Desired Values Angle-of-Attack (α) - deg.

RAG Airfoil Design Original 34% Thickness Final 28.5% Thickness
A special, relatively thick airfoil was developed composed of a 22% and an 11.7% Clark Y airfoil meshed together to form a single 28.5% thick airfoil.

Aerodynamic Characteristics of Original and Final RAG Airfoils
Lift Coefficient (CL) Drag Coefficient (CD) Direction of Flight α Spin Axis Pitching Moment (Cm) CL V RAG diameter = 2.5 in. V = 220 ft./sec. Rd = 164,000 CD Sym Configuration Original Final How much of an improvement in the lift and drag was achieved by the new airfoil is illustrated in the figure. The lift is linear with angle-of-attack and the drag is much lower at all angles. Cm Desired Values Angle of Attack (α) - deg.

Full Scale RAG Wind Tunnel Model with Final Airfoil Shape
A 2.5 in. diameter RAG with this airfoil was fabricated from aluminum and tested in the Edgewood 34 X 24 - In. Subsonic Wind Tunnel. These tests showed this RAG configuration to have an excellent lift slope and low drag up to a stall angle of 20 deg. Also, the position of the center-of-pressure of the RAG experienced very little movement with angle-of-attack.

Effect of Flight Velocity (Reynolds Number) Angle of Attack (α) - deg.
Lift Coefficient (CL) CL Spin Axis Drag Coefficient (CD) α V Direction of Flight RAG diameter = 2.5 in. Smooth Surface Sym Velocity Rd (ft./sec.) ,000 ,000 ,000 ,000 Even with improved performance of the new RAG airfoil, it still experienced aerodynamic degradation at the lower flight velocities. Note, the early stall angle-of-attack and tie associated higher drag. Staling occurs when the flow over the upper surface of an airfoil ceases to follow the contour of the surface and separate turning into a turbulent wake. This causes the lift produced by the upper surface (the major portion of lift on an airfoil) to be lost, drastically reducing the lift and increasing the drag. This “stalling” appears to occur at a Reynolds number of about 150,000 corresponding to a velocity of about 200 ft./sec. This velocity is within the RAG,s operational velocity range and must be improved. CD Desired Values Angle of Attack (α) - deg.

Effect of Boundary Layer Trips Direction RAG is Pointing
Sym B.L. Trip None Grit Wire Groove Lift Coefficient (CL) CL Direction RAG is Pointing None Drag Coefficient (CD) α . . . . Direction of Flight . . Grit . RAG diameter = 2.5 in. Velocity = 183 ft./sec. Rd = 137,000 The solution to the flow separation problem was to “trip” the boundary layer at the front surface of the airfoil changing it from laminar to turbulent and thus preventing flow separation over the rear surface. Various types of boundary layer trips were investigated including grit, a circumferential wire and a circumferential groove. These were located circumferentially around the outside of the outer airfoil, just forward of the maximum thickness. The data for these tested at a normal flight velocity are shown here. All boundary layer trips produce good lift, but the groove gives less drag and is the preferred approach. The groove also provided the near zero pitching moment desired (not shown). Wire CD Groove Desired Values

Effect of Boundary Layer Trip Groove Location
Lift Coefficient (CL) CL Direction RAG is Pointing Sym ε (in.) 0.05 0.15 0. 25 0.35 Drag Coefficient (CD) α Direction of Flight Groove Distance from Nose CD This shows the data for the grooved RAG at various locations from the nose compared to the RAG without a groove. The data shown are for a nominal RAG flight velocity. Note that the desired aerodynamics are obtained for all groove locations. RAG diameter = 2.5 in. Velocity = 183 ft./sec. Rd = 137,000 Angle of Attack (α) - deg. Desired Values

Weaponized RAG Assembly
Pre-Coined Body Tail Ring (Fuze) Pre-Coined Body High Explosive This photo shows the components and their assembly for the 2.5 in. dia., RAG with the final airfoil shape.

Aerodynamic Characteristics of Inert Munition RAG
RAG diameter = 2.5 in. V = 181 ft./sec. Rd = 137,000 Lift Coefficient (CL) Drag Coefficient (CD) Direction of Flight α Direction RAG is Pointing CL Sym Velocity (ft./sec.) 294 220 181 147 Joint Groove This plot shows the aerodynamic characteristics measured on an actual, full scale inert RAG munition. By serendipity, the mating junction between the nose ring and main body components of the RAG form a natural groove that provides the boundary layer trip groove required without any additional alterations to the projectile. The effect of the groove prevent stalling down to at least 109,000 (147 ft./sec.), well below any operational velocity for the RAG. CD Desired Value Desired Values Angle of Attack (α) - deg.

RAG Magnetic Suspension Wind Tunnel Model
2.125 in. Diameter RAG Model Steel Segments in Aluminum Body A 54mm (2.125 in.) diameter model of the RAG was tested in the Massachusetts Institute of Technology (MIT) Magnetic Suspension Wind Tunnel at various angles-of-attack and spin rates. The advantage of this type of tunnel is that the model was suspended in the tunnel by an electromagnetic field with no structural supports required that could affect the air flow over the model and whose presence would have to be accounted for by separate tare tests. The model could also be tested while spinning at 246 ft./sec. (Mach and 11,100 rpm (a non-dimensional spin rate of 0.22). Any tendency of the model to translate or rotate under the aerodynamic forces and moments was automatically compensated for by the magnetic field control system. This compensation was detected and indicated as the corresponding force and moment components: lift, drag, side force, and pitching and yawing moments. The resulting lift, drag, pitching moment and Magnus moment data showed excellent agreement with the previous Edgewood wind tunnel results

MIT Magnetic Suspension Wind Tunnel Test Magnetically Suspended
Air Flow This photo shows the RAG model in the MIT magnetic suspension wind tunnel with smoke to indicate the flow pattern over the model. This tunnel was an experimental prototype for a larger tunnel planned for the Air Force. The model was levitated by the magnetic field. It could be held at any angle-of-attack and spin rate. The strength of the magnetic field required to hold the model in place was a measure of the lift, drag and pitching moment exerted on the model by the air flow. Magnetically Suspended and Spinning RAG Model

Indoor Spark Range Screen Firing test of full scale RAG models were performed at the BRL indoor Transonic Spark Range. A spark range is kept totally dark during a test. The projectile is fired down the range and a short duration spark is set off as it passes by a station. The spark creates a large shadow of the projectile on a screen opposite the spark source and lasts only a microsecond resulting in a crisp, non-blurred image. Orthogonal cameras are located at several locations along the flight path, and whose shutters are kept open, record the shadow which depict a high resolution photo (8 ft. by 4 ft.) of the instantaneous details of the flow over the projectile. Spark Source

RAG Spark Range Shadow Graph
4 ft. 6 ft. The spinning barrel air was used to fire the RAGs down the 800 ft. long building at known initial velocities and spin rates. A plastic sabot was used to provide obturation and bore riding in the barrel. The Spark Range was used to fire projectiles that, because of their high velocities, had a flat trajectory and did not strike the ceiling. The RAG was the first low velocity projectile to still have a flat enough trajectory to strike the end of the building. Note that the flow does not separate until far back on the RAG projectile. Most of the projectiles included two pins on the trailing edge, 180 deg. apart, to measure the spin rate. These affected the spin damping. In order to employ the quadricyclic data reduction method, the RAGs had to be artificially disturbed at launch to obtain a sufficiently large initial yaw angle of 2-5 deg.

RAG Wind Tunnel and Flight Range Test Results
Term Edgewood BRL MIT Magnetic Wind Tunnel Ballistic Range Wind Tunnel RAG Diameter (in.) Velocity (ft./sec.) Spin Rate (rpm) , , ,000 Reynolds Number (Rd) x x x x 105 Lift Slope (CLα) Drag Coefficient (CD0) at α = 0 deg Magnus Moment (CNpα) This compares the RAG wind tunnel and free flight range test data results.

Straight Airfoil Wind Tunnel Models
Aspect Ratio = c/b b =8.0 in. c = 2.8 in. A series of wind tunnel tests were performed using straight airfoils. This allowed the basic aerodynamic characteristics to be compared with a thin airfoil (Clark Y) at Reynolds numbers similar to that of RAG flight velocities. This study also related to use of the RAG airfoil shape for aircraft wing applications. It was felt that the relatively high thickness ratio and exceptional performance of the RAG airfoil at low Reynolds numbers would be of value to the general aviation community as well as for Remotely Piloted Vehicles (RPV) and other small aerodynamic configurations operating at very low velocities. Two sets of linear airfoil wind tunnel models were constructed from solid aluminum. One set had the same airfoil shape as the RAG and included two sizes: a 1.4 in. chord and 8 in. span and a 2.8 in. chord and 8 in. span. The other set of models had the same chord and span dimensions but included a standard Clark Y airfoil shape. The Clark Y only had an 11.7% thickness compared to the 28.5 % thickness of the RAG airfoil. c = 1.4 in.

Comparison of Straight RAG and Clark Y Airfoils
1.2 0.8 0.4 0.0 -0.4 RC = VC γ Lift Coefficient (CL) Direction of Flight α CL Ring Airfoil (t/c = 28.5%) C C=1.4 in. Aspect Ratio = 5.7 (with end plates) t C 1.2 0.8 0.4 0.0 -0.4 Sym Velocity RC (ft./sec.) ,752 ,696 ,620 ,467 ,391 ,163 The lift coefficients as a function of the angle-of-attack are shown here for the straight RAG and Clark Y airfoils. No boundary layer trips were used in these tests. Note that both have about the same CL vs. α slope at angles-of-attack up to 10 deg for the higher velocities. The RAG airfoil, due to its greater thickness to chord ratio, experiences flow separation and lift loss at the lower velocities (i.e., Reynolds number below 100,000). CL Clark Y (t/c = 11.7%) Best Values Angle-of-Attack (α) - deg.

Effect of Reynolds Number on Lift Coefficient of Clark Y Airfoil
RC = VC γ Lift Coefficient (CL) α V C CL *Velocity = 257 ft./sec. C = 1.4 in. Aspect Ratio = 5.7 (with end plates and boundary layer notch) Sym RC 223,000* 7,000,000** Angle-of-Attack (α) - deg. ** Published Airfoil Characteristics

Comparison of Lift Coefficient for Straight RAG and Clark Y Airfoils
RC = VC γ Lift Coefficient (CL) Direction of Flight α Clark Y (t/c = 11.7%) Ring Airfoil (t/c = 28.5%) t C C CL Velocity = 257 ft./sec. RC = 223,163 C = 1.4 in. Aspect Ratio = 5.7 (with end plates and boundary layer notch) The lift coefficients as a function of the angle-of-attack are shown here for the straight RAG and Clark Y airfoils. No boundary layer trips were used in these tests. Note that both have about the same CL vs. α slope at angles-of-attack up to 10 deg for the higher velocities. The RAG airfoil, due to its greater thickness to chord ratio, experiences flow separation and lift loss at the lower velocities (i.e., Reynolds number below 100,000). Angle-of-Attack (α) - deg. Sym Configuration Ring Airfoil Clark Y

References Miller, M. C.; "Separation and Motion Analysis for the Air Launching of the SV‑SP Manned Test Vehicle from a B‑52 Mother Aircraft as Determined from Tests on 2.5% Scale Models in the NASA‑Langley 7X10‑Foot High Speed Wind Tunnel," Martin Company Engineering Report No. ER‑14299, 2 Volumes, December 1966 Flatau, A.; “Feasibility Study of the 2.5-Inch Ring Airfoil Grenade (RAG)(A Review and Summary)”, EATR-4573, December 1971 Miller, M. C.; "Surface Pressure Measurements on a Spinning Wind Tunnel Model," AIAA Journal, December 1976, Vol. 14, Pp D'Amico, W. P. and Miller, M. C.; "Flight Instability Produced by a Rapidly Spinning, Highly Viscous Liquid," AIAA, Journal of Spacecraft and Rockets, Vol. 16, No. 1, Pp 62‑64, January‑February 1979 Miller, M. C.; "Wind Tunnel Measurements of the Surface Pressure Distribution on a Spinning Magnus Rotor,"AIAA Journal of Aircraft, December 1979, Vol 16, No. 12, Pp Miller, M. C.; "Void Characteristics of Liquid Filled Cylinder Undergoing Spinning and Coning Motion," AIAA, Journal of Spacecraft and Rockets, May-June 1981, Vol. 18, No. 3, Pp 286‑288. Miller, M. C.; "Flight Instabilities of Spinning Projectiles Having Non‑Rigid Payloads," AIAA, Journal of Guidance, Control, and Dynamics; March/April 1982, Vol 5, No. 2, Pp 151‑157 Miller, M. C.; "Experimental Measurements of the Aerodynamic Surface Pressures on Spinning Bodies," Proceeding of the International Congress of Instrumentation In Aerospace Simulation Facilities (ICIASF), September 1983, Pp 117‑130 Miller, M. C.; "Surface Pressure Measurements on a Transonic Spinning Projectile," AIAA, Journal of Spacecraft and Rockets, March/April 1985, Vol. 22, No. 2, Pp 112‑118 Miller, M. C.; "Measurements of Despin and Yawing Moments Produced by a Viscous Liquid," AIAA, Journal of Guidance, Control and Dynamics, March/April 1985, Vol. 8, No. 2, Pp 282‑284 Miller, M. C.; "Liquid Filled Projectiles ‑ New Problems, New Solutions," Army RD and A Magazine November‑December 1986, Pp 24‑27 Miller, M. C.; "Laboratory Test Fixture for Non‑Rigid Payloads," Proceedings of the International Congress of Instrumentation in Aerospace Simulation Facilities, September 1989, Pp 350‑364 Weber, D. J.; “Simplified Method for Evaluating the Flight Instability of Liquid-Field Projectiles”, Journal of Spacecraft and Rockets, Jan/Feb 1994, Vol. 31, Pp Miller, M. C.; "Elimination of Viscous Liquid Fill Flight Instability by Means of Lower Viscosity, Immiscible Liquid Additive," 29th AIAA Aerospace Sciences Meeting, January 1991, Paper No. AIAA‑91‑0679 Mohamed Selmi and Thorwald Herbert, “Resonance Phenomena in Viscous Fluids Inside Partially Filled Spinning and Nutating Cylinders”, Physics of Fluids, Vol. 7, No. 1, January 1995

Extra slides

Derivation of Reynolds Number from Navier-Stokes Equations
we can rewrite the Navier-Stokes equation without dimensions: where the term Finally, dropping the primes for ease of reading: This is why mathematically all Newtonian, incompressible flows with the same Reynolds number are comparable. Notice also, in the above equation, as the viscous terms vanish. Thus, high Reynolds number flows are approximately invisid in the free-stream. The Reynolds number can be obtained when one uses the non-dimensional form of the incompressible Navier-Stokes equations for a Newtonian fluid expressed in the Lagrangian derivative: Each term in the above equation has the units of a "body force" (force per unit volume) with the same dimensions of a density times an acceleration. Each term is thus dependent on the exact measurements of a flow. When one renders the equation non-dimensional, that is when we multiply it by a factor with inverse units of the base equation, we obtain a form which does not depend directly on the physical sizes. One possible way to obtain a non-dimensional equation is to multiply the whole equation by the following factor: where: is the mean velocity, or , relative to the fluid (m/s). is the characteristic length (m). is the fluid density (kg/m³). If we now set:

Upgraded Test Fixture for Non-Rigid Payloads

Measures Projectile Spin Rate and Angular Motion During Flight
Yaw Sonde Measures Projectile Spin Rate and Angular Motion During Flight Direction Projectile is Pointing Reference Angle Light sensors on opposite sides of the nose detect occurrence and angle of sun light Direction of Sun Light Sun light sensed every revolution of the projectile measures projectile spin rate Sun light angle every revolution of the projectile measures projectile yaw angle

155mm Point Recognition Projectile (PRP) “Nite-Stick” Projectile
Rupture Disk Diphenyl Oxalate + Dye Hydrogen Peroxide During Operation Desert Storm (ODS), it was difficult for the military to identify particular ground locations due to the absence of any distinct features on the barren landscape of Kuwait/Iraq. This project involved a 155mm artillery projectile that could accurately hit a known point and mark the impact with a visual marker that could be observed at night by any adjacent troops or aircraft. Referred to as the Point Recognition Projectile (PRP), it contained a luminescence liquid (used in night-sticks) for night time operations. The payload was delivered via a modified M687 projectile. The luminescent liquid had two precursor liquids, an oxalate + dye and an activator that were loaded into the M20 and M21 canisters, respectively and mixed during flight similar the basic M687. The result was a 1.2 gallon nite stick compared to 1 tablespoon of liquid in a 6 inch glo-stick. 256 X volume of nitestick. The dye determined the color of the luminescent glow (in this case, green). The original M687 contained Methylphosphonyl Difluoride (DF) and Osopropyl Alcohol Amine (OPA) that when mixed produce the nerve agent Saren (GB). M mm Projectile and M20/M21 Canisters Glo-Stick = 1 tbsp. PRP = 1.2 gal. = 250 Glo-Sticks

PRP Payload Release at Night
6 in. Air Gun Muzzle 100’ X 25’ Wall The ARB tested the payload composition on the Laboratory Test Fixture for Non-Rigid Payloads to assess its potential for a flight instability due to the viscous nature of the liquid. No detrimental stability problem was noted. In addition, a night test was performed at Edgewood by firing a payload from the Aero Group’s 6-inch spinning barrel air gun. The entire area was illuminated as shown in this photo. That is a 25 ft. high, 100 foot long concrete wall in the background. Several dozen rounds of each type were assembled at Edgewood and shipped to the ODS combat zone. The project engineer, Pat Nolan, was present in Kuwait when one of the luminescent rounds was fired at night. A military forward observer yelled into his radio. "What in the hell was that?" The round had worked perfectly, illuminating the entire surrounding area.

Flow Around Autorotating Shape Film
M Magnus Rotor wmv ( 0 min. 50 sec.): Cylindrical Magnus autorotor in smoke flow visualization wind tunnel – different speeds (illustrates shed vortex)

Autorotating (Self Dispersing) Bomblets
An example of using the autorotating phenomena in practice is the BLU-26 bomblet. This is a spherical shape with four driving vanes. It is released in large numbers from an aircraft dispenser. The spin arms the bomblets and causes them to glide dispersing them over a large area on the ground. At ground impact a fuze sets off the fragmenting explosive. BLU-26 Bomblets BLU-26 on Spin Yoke Mount in Wind Tunnel

Glide Angles for Different Autorotating Shapes
All autorototers produce both a lift and a drag force. Rather than falling straight down, they glide at an angle to the vertical that is proportional to their lift to drag ratio. The larger the lift to drag ratio, the flatter the glide angle. This shows the range of glide angles from a sphere with 22 deg. flight path to the vertical to a two part Savonius rotor with a 76 deg. glide angle. End plates increase the lift to drag ratio and enhance the flight stability.

Missile Warhead with Autorotating Self Dispersing Bomblets
Here is an Honest John warhead cut-away with bomblets.

Typical Ground pattern for Autorotating Self Dispersing Bomblets
An 800 ft. diameter pattern on the ground is obtained from a single warhead.

Flow Field Around Magnus Autorotor

Method to Measure Surface Pressures on Magnus Autorotor
With the successful measurements of the surface pressures on a spinning right circular cylinder in cross flow, the next step was to extend the technique to measure the surface pressure distribution over a spinning Magnus rotor. The same basic model used in the previous test was modified to represent a typical four vane cylindrical Magnus rotor. In this case, the full span vanes presented protuberances and the flow, while unsteady, was periodic with the flow field pattern being repeated four times every revolution. Multiple vent holes were required to cover a quadrant of the irregular rotor surface. A total of 8 vent holes were used in the model covering the main portion of the spin vanes and cylindrical body in between. Another difference between the Magnus rotor model and the prior smooth cylinder model was that the vent holes through the vane area had extended lengths.

Magnus rotor Surface Pressure Wind Tunnel Model
The 5.2 in. diameter model was tested at 2,050 rev./min. corresponding to the steady state spin rate for the Magnus rotor at the test velocity of 100 ft./sec. As before, the model was spun by an electric motor mounted above the tunnel. The 8.5 in. span model also had 9.3 in. diameter circular end plates to prevent tip losses and maintain a constant spanwise pressure distribution. The test spin rate was determined by testing a similarly configured model on a free-spinning yoke mount in the same wind tunnel. The yoke was attached to a pyramidal strain gage balance located below the floor of the tunnel and the lift, drag and steady state spin rate measured at various free stream velocities.

Surface Pressure at Vent Hole 5 (Top of Driving Vane)
Over One Revolution Vent Hole 5 The testing procedure was to measure the pressure acting at a single vent hole and then sequentially setting the non-spinning, model core at incremental angles until a complete circuit of the model circumference was attained. This shows the pressure at vent hole 5 over one revolution. It is as if a pressure tap at location 5 measured the pressure at this point as the model rotated over one revolution. This would be beyond the capability (time response) of any existing pressure transducer that could not react to the pressure changes in the short time available at each angle.

Surface Pressure on Spinning Magnus Autorotor
The testing procedure was to measure the pressure acting at a single vent hole and then sequentially setting the non-spinning, model core at incremental angles until a complete circuit of the model circumference was attained. That hole was then closed-off, another vent hole opened and the process repeated. Once the pressure distribution for all of the vent holes had been obtained, the pressure distribution over the entire model was plotted for a single rotational angle (corresponding to a particular instant of time). For the four-vane rotor configuration, the pressure was repeated every quarter revolution. The continuous nature of the measured pressure distribution allowed the pressure distribution to be plotted for any time interval no matter how small. Pressure data were plotted for every sec, but because of the periodic nature of the flow, they could have been plotted for every sec. or any other time increment. This explains how an unsteady flow situation could be measured by a steady state transducer. These plots depicted the extremely high pressure spike and lift created by the strong vortex formed and shed by the retreating vane. The pressures were integrated over the surface of the autorotor to obtain the lift and drag forces. The ability to present the resulting forces at such small time intervals revealed the sinusoidal nature of the lift and drag as well as their phase relation. Another interesting finding was that the non-spinning and spinning rotor have completely different flow fields, aerodynamic pressures and forces. This project represented the first, and to date, the only, measurement of the surface pressures on a spinning Magnus rotor.

Flow Field, Surface Pressure and Forces on
Spinning Magnus Rotor at 22.5 Degree Rotation Angle Lift Pressure Flow A 4 in. diameter model was tested in the University of Notre Dame smoke wind tunnel where the detailed flow field over the spinning model at various free stream velocities was recorded by a high-speed camera. These data allowed a composite picture to be made of the flow field, pressure distribution and resulting lift and drag forces acting on the rotor at a particular instant in time which were very helpful in illustrating and interpreting the cause and effect of the various Magnus phenomena. Drag

Effect of spin on Pressures and Forces

Surface Pressures on Spinning Cylinder in Cross flow

Flow Field Around Magnus Autorotor

Typical Shock Wave Pattern of Projectile at Transonic Speed
Front Shock Rear Shock The consensus of the aeroballistic community held that the projectile was “marginally stable” at transonic launch conditions. If the round experienced a relatively large yaw disturbance at launch, it would assume a large angle yawing motion with an associated high drag resulting in a short range flight. This unstable flight was due to the combined effect of a low gyroscopic stability factor and a large Magnus moment, both exacerbated by the long body and boattail length. The marginal stability of the M483, even after it was fitted with a shortened boattail as the M483A1, made it susceptible to a payload induced instability as was the case with the XM761. Wake

A 130% scale model of the M549 was designed and built.
While the same two-part model arrangement, consisting of a stationary central core and a spinning outer shell, used in the earlier spinning cylinder tests was employed, a more efficient and easier method of operating the seal mechanism was required. Following those tests, a series of experiments were performed with the cylinder model to evolve a more robust, accurate and efficient rubbing seal design. These tests resulted in the development of a smaller seal (half the size of those used previously), an improved rubber O-ring material impregnated with lubricant (negating any need for a separate lubricant application mechanism), a new O-ring cross sectional shape (possessing better sealing), and the use of pneumatics to remotely engage and disengage the pressure taps.

Sliding Seal Details These tests resulted in the development of a smaller seal (half the size of those used previously), an improved rubber O-ring material impregnated with lubricant (negating any need for a separate lubricant application mechanism), a new O-ring cross sectional shape (possessing better sealing), and the use of pneumatics to remotely engage and disengage the pressure taps. A scanivalve inside the model core was used to select a particular pressure tap position, direct the pneumatic pressure to the seal, and route the pressure signal to the monitoring console. Both operations could be done remotely from the test console located outside the tunnel test section without shutting down the wind tunnel.

Model in Test Section Testing in the Ames 14 - Ft. Transonic Wind Tunnel. Here is the model installed in the tunnel test section.

Nutation Rate ω ≈ Cmα pIx ω = 2I 1 + 1/τ Where: τ = 1/s s = p2Ix2 4IMa
C mα ρV2 S d 2 ω ≈ Cmα

λ = (1 + τ) τ Mq Mpa 2I Ix Coning Angle = A eλt

Typical RAG Trajectory
Velocity - ft./sec. RAG Diameter = 2.5 in. Length = 1.4 in. Weight = 0.3 lbs Initial Velocity = 225 ft./sec. Initial Spin Rate = 6,000 rpm Initial Launch Angle = 6 deg. Angle-of-Attack, Flight Path Angle - deg. Range Height Horizontal RAG pointing Velocity Angle-of-Attack Flight Path Angle Height - meters The data obtained from the wind tunnel were used to compute the trajectory for the RAG under various launch conditinos. This set of graphs illustrate the trajectory term values for a typical RAG firing . A 6 deg. launch angle produces a 430 meter flight to ground impact. The initial 225 ft./sec. velocity decreases to 185 ft./sec. during the 7 sec. flight. Note how the angle-of-attack automatically follows the change in the flight path angle and reaches a maximum angle-of-attack of only 8 deg. while the flight path angle stays between 6 and -2 deg. A maximum height of only 45 meters (148 ft.) is reached - a very flat trajectory! Range - meters Time - sec.

Arena RAG Aerodynamic Characteristics
Velocity = 220 ft./sec. Reynolds number = 328,723 0.6 0.4 0.2 -0.2 Lift Coefficient (CL) Drag Coefficient (CD) Direction of Flight α Direction RAG is Pointing Pitching Moment (Cm) CL V 0.4 0.2 CD The airfoil was made exceptionally thick in order to contain as much explosive as possible - approaching a 30% thickness to chord ratio. Again, this is extremely large compared to most aircraft wing thicknesses of around 10% - 15%. This shows the lift, drag and pitching moment coefficients for the original RAG airfoil shape at a typical flight velocity. The green lines indicate what satisfactory data should look like. Note the low, erratic and non-linear lift, the high drag and large pitching moment - all undesirable. Designing an airfoil to operate at the small size an slow velocity of the RAG is not simple, especially if it is a relatively thick airfoil. The Reynolds numbers corresponding to these low velocities and small projectile are several orders of magnitude smaller than for a typical airplane and for any available airfoil data. 0.10 0.05 -0.05 -0.10 Cm Desired Values Angle-of-Attack (α) - deg.

Comparison of Upright and Inverted RAG Airfoil
1.2 0.8 0.4 0.0 Lift Coefficient (CL) Direction RAG is Pointing CL α Direction of Flight α V Aspect Ratio = 5.7 1.2 0.8 0.4 0.0 Sym Velocity Rd (ft./sec.) ,752 ,696 ,620 ,467 ,163 These plots show the lift coefficient vs. angle-of-attack for the straight RAG airfoil in both an upright and inverted attitude. The upright airfoil represents the upper portion of the ring airfoil while the inverted attitude represents the lower portion of the ring airfoil. Note the switch in the effect of Reynolds number between these two results. The upright airfoil gives the best data at the higher Reynolds numbers, whereas the inverted airfoil gives the best data at the lower Reynolds numbers. CL Angle-of-Attack (α) - deg. Best Values

Straight RAG Airfoil Data Direction Airfoil is Pointing
Sym Airfoil Chord Span Aspect Velocity Rd (in.) (in.) Ratio (ft./sec.) RAG RAG RAG ,163 w/Groove Lift Coefficient (CL) Direction Airfoil is Pointing α Direction of Flight CL These are wind tunnel data measured on models of the basic RAG a straight airfoil at about the same Reynolds number. The earlier stall for the larger cord airfoil may be due to its lower aspect ratio. Best Values

RAG vs. Straight RAG Airfoil Data
Lift Coefficient (CL) CL RAG Direction RAG is Pointing α Direction of Flight 1.2 0.8 0.4 0.0 CL RAG Airfoil (Upright) Aspect Ratio = 5.70 These are wind tunnel data measured on models of the basic RAG a straight airfoil at about the same Reynolds number. 1.2 0.8 0.4 0.0 Best Values CL RAG Airfoil (Inverted) Aspect Ratio = 5.70 Angle-of-Attack (α) - deg.

Weaponized RAG Assembly
Pre-Coined Body Tail Ring (Fuze) Pre-Coined Body High Explosive This photo shows the components and their assembly for the 2.5 in. dia., RAG with the final airfoil shape.

RAG Magnus Wind Tunnel Test
Air Turbine Free Spinning, Full Scale RAG Wind Tunnel Model Wind Shield This is rig used to measure the spin damping of the RAG. The full scale, RAG model was spun up to a high spin rate (8,000 rpm) by a compressed air turbine. The air was cut-of and the RAG was allowed to freely spin down due to aerodynamic effects. The tare effect of the interior RAG mounting spokes were subtracted out resulting in the spin damping of the RAG alone.

RAG Pitch/Yaw Damping Wind Tunnel Test
Free Rotating Strut Full Scale, RAG Wind Tunnel Model This shows the pitch damping rig. Since the RAG is a symmetric shape, the pitch and yaw are the same and a yaw rig in the wind tunnel can measure the pitching moment. A tail was attached to provide yaw stability to the otherwise neutral stability of RAG. The RAG model and tail was deflected to a large yaw (sideward) angle and released. The model oscillated with diminishing angles until stationary with yaw recorded as a function of time. The tail was tested alone and its effect subtracted from the RAG/tail combination data to provide the RAG yaw (pitch) damping. Stabilizing Fin

RAMP Transonic Wind Tunnel Test Results
(Effect of Airfoil Orientation) Subsonic Transonic Supersonic Nominal Muzzle Velocity = 700 ft./sec. As noted previously, the drag coefficient is affected by Mach number. This graph of drag coefficient vs. mach number illustrates how the blunt nosed RAG had lower drag at subsonic velocities but had a high drag at velocities greater than Mach 1 (supersonic speeds). By contrast, tests of the RAG turned around to have the sharp edge forward produced high drag at subsonic speeds and lower drag at supersonic speeds. Velocity = 1,000 ft./sec.

Low Reynolds Numbers in Practical Use

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