# Takeoff Performance Continued – FAR Part 25 and Examples

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Takeoff Performance Continued – FAR Part 25 and Examples
AOE 3104 Lecture 14: Takeoff Performance Continued – FAR Part 25 and Examples E. D Crede* Aerospace & Ocean Engineering Department Virginia Polytechnic Institute & State University *Special thanks to M. C. Cotting for preparing this presentation.

Lecture 14 Outline FAR, Part 25 Runway Conventions
T/O Data Standardization Doolittle’s Raid Picture is of a Piper Cub taking off of a Navy ship during WW II to perform reconnaissance for artillery

Takeoff Performance Takeoff has two distinct phases:
Accelerate (on the ground) to a desired speed. Climb to a minimum height, at a required minimum speed, to clear potential obstacles: 35 ft height (civil transports) 50 ft height (general aviation and military) Required runway length: Total distance to point where specified height is reached. In US airspace, takeoff performance is dictated by FAR (Federal Aviation Regulation) Part 25.* *Airworthiness for Transport Category Aircraft

Takeoff Diagram Picture adapted from Shevell, shows major speed points along takeoff run. Takeoffs points are marked by speeds instead of distances b/c it is easier for the pilot to watch his airspeed meter than to try and estimate distances while on his roll. If he starts at the end of the runway each time the speeds and distances should be calibrated.

Takeoff Speed Definitions
VMCG V1 VR VLOF V2 Aircraft Pilot Manuals will list (at least): V1, VR, and V2 Values are mandated by FAR Part 25. Values are functions of takeoff weight, altitude, temperature, wind, and runway slope. Other critical speeds are derived from these, to ensure safe margins above Vstall and Vmc both in free air and in ground effect.

Vstall Stall Speed: The minimum speed at which enough lift can be generated to maintain flight. It’s important to note that the airspeed indicator will read KEAS (Knots, Equivalent Airspeed) or KCAS (Knots Calibrated Airspeed) and not TAS (true airspeed in Knots). Therefore just listing a stall speed is not sufficient for a pilot. As engineers we must be sure to list it as read in the Cockpit when writing the operators manual. Hence the scaling from TAS to KEAS. This same scaling should be applied to all velocities when listed in an operating manual. Thinking that you are taking off from the ground and therefore KEAS = TAS is not correct. It’s only a good assumption if you are at sealevel, otherwise the KEAS read by the airspeed indicator will not be TAS. On this plot lifting force is nondimensionalized by weight, so straight and level flight is where LF=1. V_s = \sqrt{\frac{2W}{C_{Lmax}S \rho}} V_s (KEAS) = V_s (TAS) \sqrt{\frac{\rho_{alt}}{\rho_{sl}}}

VMCG Minimum Controllable Ground Speed: It is the minimum speed on the ground for which a sudden, single engine failure (with the remaining engines at takeoff power) does not result in loss of primary flight control.

V1 Decision Speed: The speed at which there is no longer enough runway to stop: V < V1: An engine failure means stopping on the runway. V > V1: Committed to take off, regardless of a single engine failure (for multiengine aircraft). V_R\ge V_1 \leq V_{MCG}

VR Rotation Speed: The proper speed to start the rotation for liftoff.
V_R \ge 1.05 V_{mca} Vmca : Minimum controllable airspeed with gear retracted. (Note: Multi-engine aircraft must remain controllable in flight, even after loss of an engine.)

VLOF Liftoff Speed: The speed at which the aircraft lifts off the ground. (The aircraft does not leave the ground immediately at rotation.) V_{LOF}\geq 1.10 V_{mu}&& \mbox{all engines operational}\\ V_{LOF}\geq 1.05 V_{mu}&& \mbox{one engine out}\\ Vmu : Airspeed at and above which the airplane can safely lift off the ground and continue the takeoff – not necessarily VR.

V2 Takeoff Safety Speed: The proper speed for climb-out on takeoff (minimum speed at specified obstacle height): 1.2 Vstall: Civil jets and two-engine civil turboprops 1.15 Vstall: Four-engine civil turboprops 1.10 ~ 1.05 Vstall: Military and general aviation V_{2} \geq && 1.10 V_{mca}\\ V_{2} \geq && 1.2 V_{stall}\\

Runway Conventions Runways are marked so that pilots know how far down the runway they are, and can therefore judge how much runway has been used for takeoff. 59’ 120’ Runway Centerline Markings Note these are example markings. Large commercial fields look more like the top runway, smaller general aviation fields look like the lower runway.

Balanced Field Length The FAR takeoff field length (or balanced field length) accounts for engine failure situations. Should an engine fail during the takeoff roll at the decision speed V1, the pilot may elect to: continue the takeoff on the remaining engines shut down all engines and apply brakes "Airworthiness Standards: Transport Category Airplanes," FAR Pt. 25 (FAA, February 1, 1965)

Determining Field Length

FAR Part 25 T/O Distance Lift-off distance:
The function f is depicted in a chart to follow. FAR Part 25 adds 15% to the lift-off distance to estimate total takeoff distance \sigma = \frac{\rho}{\rho_{s}} d_{LO}= f\left( \frac{W^2}{\sigma S C_{Lmax} T } \right) d_{TO}=1.15 d_{LO}

Chart from FAR Part 25

Factors Affecting T/O Distance
Thrust Variations Wing Loading CLTO Density Altitude Winds Runway Slope Runway Condition Pilot Technique Most significant factor Toughest to control

Takeoff Data Standardization
Takeoff testing of aircraft does not occur in an idealized world. Standardization refers measured takeoff distance to a standard altitude and weight, with zero wind on a level runway. (Empirically derived.) Four steps, applied in order: Runway slope correction Wind correction Weight correction Altitude correction Review the two methods Obtain a distance for each method Standardize each one

Slope Correction dslope: Takeoff distance found from aircraft test
dlevel: Takeoff distance, corrected for runway slope µ: Runway slope from horizontal (+/- uphill/downhill) Review the two methods Obtain a distance for each method Standardize each one

Wind Correction dcalm: Takeoff distance, corrected for wind
VW : Wind component along runway (+ for headwind) VTO : Takeoff groundspeed

Weight Correction dWnom : Takeoff distance, corrected for weight
Wact : Actual takeoff weight Wnom : Nominal takeoff weight

Density Correction ½SL : Sea-level, standard day air density.
½TO : Air density during takeoff. dSL: Takeoff distance, referred to SL ISA conditions. Note this is as much about takeoff altitude as it is about hot vs cold day, etc.

Standardized T/O Distance
Putting it all together… Given a measured takeoff distance dmeas, compute the standardized takeoff distance dSL. This is the takeoff distance in nominal conditions (level runway, no wind, standard weight, and standard, sea-level density).

Example: T/O Results for T-38
Takeoff Airspeed - VTO The “Football” Just because you calculate a liftoff distance, does not mean the plane will take off there!!! Squares represent where takeoff occurred. The Distribution is due to pilot technique NOMINAL CURVE Standardized Ground Roll Distance - dSL

References FAA: Shevell, Richard S., Fundamentals of Flight, Second Edition, Prentice Hall, 1989

Jimmy Doolittle’s Raid
Captain Frank Lowe (USN) predicted that Army twin-engine bombers could be launched from a carrier, under the right conditions. Lieutenant Colonel Jimmy Doolittle (USA) planned and executed the raid using 16 modified B-25B's of the 34th BS, 17th BG flying from the deck of the USS Hornet (CV 8) nm from Tokyo The raid took place after two months of planning and training with 16 all- volunteer crews, in the aftermath of the attack on Pearl Harbor.

Jimmy Doolittle’s Raid
The two key impacts of the raid, according to J. Doolittle, were: “[To] give the folks at home the first good news that we'd had in World War II [and] From a tactical point of view, it caused the retention of aircraft in Japan for the defense of the home islands when we had no intention of hitting them again, seriously in the near future. Those airplanes would have been much more effective in the South Pacific where the war was going on.”

Jimmy Doolittle’s Raid
B-25B bombers on the deck of the CV-9, USS Hornet 2 US Aircraft carriers were sent on the mission. To protect the carriers, and save weight on fuel, the bombers did not plan to return to the carriers (and give their position away): Crews were to ditch the aircraft in China and Russia, saving fuel weight. A Japanese boat discovered the fleet on the way to the takeoff point. The planes had to launch 400 miles farther away than planned.

Jimmy Doolittle’s Raid
The premature mission launched in 30 ft seas. 15 of the 16 bombers were able to attack their target; none were shot down. Of the 80 aircrew on the mission, 64 survived and were able to fight again in WW II.

The Technical Challenge
How can a B-25 Mitchell take off from an aircraft carrier? Early carrier -- no steam catapults. Nominal takeoff run for a B-25 : 1,400 ft Maximum takeoff run on the carrier: 467 ft

(note these numbers are rounded)
Normal B-25 Weights Nominal takeoff weight: 32,000 lbs Crew: 6 men (165 lbs per man) : 1000 lbs Payload (bombs): 3200 lbs Fuel (1000 gallons): ~6750 lbs (note these numbers are rounded)

Raiders Weights Actual takeoff weight: 31,000 lbs
Crew: 5 men (165 lbs per man) : 825 lbs Payload (bombs): 2000 lbs Fuel (1241 gallons): ~8375 lbs Except for one gunner’s station, all guns were replaced with painted broom handles. The heavy Norden bombsight was removed and replaced with metal crosshairs.

Trimming Takeoff Distance
Only 1000 lbs of T/O weight removed. Where did the T/O distance reduction come from? 30 mph headwind Full flaps on T/O (increasing CLmax from 1.92 to 2.92)

Standard B-25 Takeoff Using Anderson’s “constant force” approximation for T/O distance (in US units): d_{to}\approx 1.44 \frac{W^2}{g \rho S C_{Lmax} (550 T)/V_{TO}} \begin{tabular}{ccc} $W=32,000$ lbs & $V_{TO}=161$ ft/sec (110 MPH)& $g= ft/sec^2$\\ $S=610$ $ft^2$ & $T = 2 * 1700$hp ( hp engines) & $\rho =$ (sea level density) \\ $C_{Lmax}=1.92$ & & \\ \end{tabular}

Lower Flaps to Full B-25 Lowering flaps increases CLMax from 1.92 to 2.92.

Mission safety requirement: VW > 20 MPH.
Headwind Takeoff VW = 30 ft/sec (20 MPH) d_{wnd}= d_{to}\left(\frac{V_{to}-V_{wind}}{V_{to}}\right)^{1.85} Mission safety requirement: VW > 20 MPH.

Jimmy Doolittle’s Raid

B-25 References http://www.specwarnet.net/miscinfo/doolittle.htm

What Next? Landing Distance Week #5 Reading: Anderson: Section 6.15
Marchman: Chapter 7