1. Workshop: Digital DATCOM
Dr. Bilal Ahmed Siddiqui

2. Contents Introduction to Aerodynamics Stability and Control
USAF DATCOM
Digital DATCOM
Enhancements
Missile DATCOM
Sample Cases
Some Practice
What’s More?

3. Aerodynamics
Aerodynamics : interplay of air & bodies trying to move through it
Air resists some motion…and aids some motion
Important to understand this interplay to harness it
Formal study of aerodynamics began 300 years ago, so it is a relatively young science!
Informally, we have been harnessing wind since a long time…….really long

4. Ancient Egyptian Aerospace!
[1290 BC]

5. But Preserved History is different…
In 1799, Sir George Cayley became the first person to identify the four aerodynamic forces of flight
In 1871, Francis Herbert Wenham constructed the first wind tunnel, allowing precise measurements of aerodynamic forces.
In 1889, Charles Renard became the first person to predict the power needed for sustained flight.
Otto Lilienthal was the first to propose thin, curved airfoils that would produce high lift and low drag.
However, interestingly the Wright brothers, mechanics – not engineers- found most of the initial work flawed and did something else….a hundred years after Cayley.

6. 27th of Ramadhan….a Friday
On Dec 15, 1903 (corresponding to Hijri date above), Wilbur and Orville Wright made history after failing to achieve it for 3 years.
Cycle mechanics, enthusiastic about flight, they designed airplanes based on aerodynamic data published by Leinthall and Langley.
All attempts were splendid failures, so they began to doubt the crude theories of their times.
They built themselves a windtunnel and started testing airfoils. To their surprise, they obtained reliable results and the rest is history.

7. The [W]Right [Bi]Plane

8. Forces and Moments in Flight
Straight level flight means constant velocity and altitude.
There are four main forces which govern straight level flight
For level flight, Lift=Weight and Thrust=Drag
In other words, 𝑇 𝑊 = 𝐿 𝐷 in level flight
Except weight, all other variables depend
on Aerodynamics.
Aerodynamics also causes moments in all three axes

9. Aerodynamic Moments
Aerodynamics also causes moments in all three axes.
Performance of aircraft depends on aerodynamics!

10. Source of all Aerodynamic Forces &Moments
No matter how complex the body shape and flow, the aerodynamic forces and moments on the body are due to only two basic sources:
Pressure distribution p over the body surface
Shear stress distribution τ over the body surface
Pressure varies with velocity of air over the surface and acts normal to it. For incompressible, inviscid flow, it follows Bernoulli principle.
Shear stress is due to friction in the boundary layer and acts tangent to the surface. Typically 𝜏≪𝑝

11. Net Effect of Pressure and Shear Distribution
Each body shape and flow condition creates unique p & τ distribution
The net effect of the p and τ distributions integrated over the complete body surface is a resultant aerodynamic force R and moment M on the body.
Far ahead of the body, the flow is undisturbed and called free stream.
V∞ = free stream velocity=flow velocity far ahead of the body.

12. Components of Aerodynamic Force R
Let distance between leading and trailing edges be “chord”=c
“Angle of attack” is the angle between 𝑉 ∞ and c
R can be resolved into two sets of components: either wrt 𝑉 ∞ or c
𝐿=𝑙𝑖𝑓𝑡=𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑉 ∞ 𝐷=𝑑𝑟𝑎𝑔=𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑉 ∞
𝑁=𝑛𝑜𝑟𝑚𝑎𝑙 𝑓𝑜𝑟𝑐𝑒=𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 𝑡𝑜 𝑐 𝐴=𝑎𝑥𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒=𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑡𝑜 𝑐
But, {L,D} and {N,A} are related through 𝛼
𝐿=𝑁 cos𝛼−𝐴 𝑠𝑖𝑛α
𝐷=𝑁 𝑠𝑖𝑛𝛼+𝐴 𝑐𝑜𝑠𝛼

13. Source of {N,A} and {L,D}
Pressure p, shear τ , surface slope θ are functions of path length s.
For a unit span l=1, the forces are
𝑁=− 𝐿𝐸 𝑇𝐸 𝑝 𝑢 𝑐𝑜𝑠𝜃+ 𝜏 𝑢 𝑠𝑖𝑛𝜃 𝑑 𝑠 𝑢
+ 𝐿𝐸 𝑇𝐸 𝑝 𝑙 𝑐𝑜𝑠𝜃− 𝜏 𝑙 𝑠𝑖𝑛𝜃 𝑑 𝑠 𝑙
𝐴= 𝐿𝐸 𝑇𝐸 −𝑝 𝑢 𝑠𝑖𝑛𝜃+ 𝜏 𝑢 𝑐𝑜𝑠𝜃 𝑑 𝑠 𝑢
+ 𝐿𝐸 𝑇𝐸 𝑝 𝑙 𝑠𝑖𝑛𝜃+ 𝜏 𝑙 𝑐𝑜𝑠𝜃 𝑑 𝑠 𝑙

14. Source of Aerodynamic Moment
The aerodynamic moment exerted on the body depends on the point about which moments are taken.
Moments that tend to increase α (pitch up) are positive, and moments that tend to decrease α (pitch down) are negative.
Moment about the leading edge is simply the forces x moment arms.
𝑀 𝐿𝐸 = 𝐿𝐸 𝑇𝐸 𝑝 𝑢 𝑐𝑜𝑠𝜃+ 𝜏 𝑢 𝑠𝑖𝑛𝜃 𝑥− 𝑝 𝑢 𝑠𝑖𝑛𝜃− 𝜏 𝑢 𝑐𝑜𝑠𝜃 𝑦 𝑑 𝑠 𝑢
+ 𝐿𝐸 𝑇𝐸 −𝑝 𝑙 𝑐𝑜𝑠𝜃+ 𝜏 𝑙 𝑠𝑖𝑛𝜃 𝑥+ 𝑝 𝑙 𝑠𝑖𝑛𝜃+ 𝜏 𝑙 𝑐𝑜𝑠𝜃 𝑦 𝑑 𝑠 𝑙
In equations above, x, y and θ are known functions of s for given shape.
A major goal of aerodynamics is to calculate p(s) and τ(s) for a given body shape and freestream conditions ( 𝑉 ∞ and α) aerodynamic forces/moments

15. Getting rid of the Dimensions…convenience
It will become clear later that it is of benefit to non-dimensionalize forces and moments.
Let 𝜌 ∞ be the free stream air density and S and l be reference area and reference length respectively.
Dynamic pressure, 𝑄 ∞ = 1 2 𝜌 ∞ 𝑉 ∞ 2
Lift coefficient, C L = L Q ∞ S
Drag coefficient, C D = D Q ∞ S
Lift coefficient, C L = M Q ∞ S𝑙
Axial and normal force coefficients are similarly defined.
Coefficients makes the math manageable. An aircraft with a 50m2 wing area and weight of 10,000kg at sea level cruise will have a lift coefficient of 0.3 at a speed of 100m/s, rather than a lift of 9.8x104 N.

16. Reference Area and Length
In these coefficients, the reference area S and reference length l are chosen to pertain to the given geometric body shape
E.g., for an airplane wing, S is the planform area, and l is the mean chord length c.
for a sphere, S is the cross-sectional area, and l is the diameter
Particular choice of reference area and length is not critical
But, when using force and moment coefficient data, we must always know what reference quantities the particular data are based upon.

17. Parameters which influence Aerodynamics
By intuition, the resultant aerodynamic force R should depend on
Freestream velocity 𝑉 ∞ (faster air  more force and moment)
Freestream density 𝜌 ∞ (denser air  more force and moment)
Freestream viscosity 𝜇 ∞ (viscosity  shear stress)
Size of the body (more reference area and length  more force and moment)
Compressibility of air (density changes if flow speed is comparable to speed of sound 𝑎 ∞ )
Angle of attack 𝛼
Therefore,
𝐿= 𝑔 𝑙 ( 𝜌 ∞ , 𝑉 ∞ ,𝑆,𝑐, 𝜇 ∞ , 𝑎 ∞ ,𝛼)
𝐷= 𝑔 𝑑 ( 𝜌 ∞ , 𝑉 ∞ ,𝑆,𝑐, 𝜇 ∞ , 𝑎 ∞ ,𝛼)
M= 𝑔 𝑚 ( 𝜌 ∞ , 𝑉 ∞ ,𝑆,𝑐, 𝜇 ∞ , 𝑎 ∞ ,𝛼)
for some nonlinear functions 𝑔 𝑙 , 𝑔 𝑑 and 𝑔 𝑚 .
This is not useful as this means a huge combination of parameters needs to be tested or simulated to find the relationships necessary for designing aerodynamic vehicles and products.

18. Dimensional Analysis
Fortunately, we can simplify the problem and considerably reduce our time and effort by first employing the method of dimensional analysis.
Dimensional analysis is based on the obvious fact that in an equation dealing with the real physical world, each term must have the same dimensions.
So it is equivalent to find relationships between dimensionless groups of parameters rather than the parameters themselves.
We can show that force and moment coefficients depend on the Reynold and Mach numbers and flow angles only, i.e.
𝐶 𝑙 = 𝑓 𝑙 ( 𝑀 ∞ ,𝑅 𝑒 ∞ ,𝛼)
𝐶 𝑑 = 𝑓 𝑑 ( 𝑀 ∞ ,𝑅 𝑒 ∞ ,𝛼)
𝐶 𝑚 = 𝑓 𝑚 ( 𝑀 ∞ ,𝑅 𝑒 ∞ ,𝛼)
i.e. fl, fd and fm.
Notice that all parameters are dimensionless!
Notice that we have reduced the number of parameters from 7 to just 3!
There may be other “similarity parameters” other than these 3, depending on problem.
𝑅 𝑒 ∞ = 𝜌 ∞ 𝑉 ∞ 𝑐 𝜇 ∞
𝑀 ∞ = 𝑉 ∞ 𝑎 ∞

19. Flow Similarity
Consider two different flow fields over two different bodies. By definition, different flows are dynamically similar if:
Streamline patterns are geometrically similar.
Distributions of 𝑉 𝑉 ∞ , 𝑝 𝑝 ∞ , 𝑇 𝑇 ∞ etc., throughout the flow field are the same when plotted against non-dimensional coordinates.
Force coefficients are the same.
If nondimensional pressure (CP) and shear stress distributions ( 𝜏 𝑄 ∞ ) over different bodies are the same, then the force and moment coefficients will be the same.
In other words, two flows will be dynamically similar if:
1. The bodies and any other solid boundaries are geometrically similar for both flows.
2. The similarity parameters are the same for both flows.
This is a key point in the validity of wind-tunnel testing.

20. Wait a Minute…Too much Math 
Hey, this was supposed to be fun

21. So how to solve these equations?
Obviously, this is pretty darn hard mathematics!
So how to solve these equalities and inequalities?
No closed form analytic solution (except simplest cases)
One way is the wind tunnel!
1/3 scale model of space shuttle in NASA’s 40-foot-by-80-foot WT
Mercedes-Benz’s Aeroacoustic Wind Tunnel
Educational Wind Tunnel

22. Computational Fluid Dynamics (CFD)
An alternate technique is to divide the flow into small boxes (grid) and solve the full Navier Stokes (or simplifications) equations at every point numerically.
This is now possible with high speed computing.
But it is not really as useful as thought.
In the end, it is really Colorful Fluid Dynamics. A lot of colors which may mean something…or nothing.
Needs a lot of calibration and EXPERTISE.
Also, not feasible for trade studies and initial design.
Slow solutions. One design iteration can take days.

23. Between Wind Tunnels and CFD
So, wind tunnels are expensive and time consuming.
So is CFD. Both requires experts to interpret results.
You really can’t DESIGN your aircraft in WT/CFD.
Here is where “engineering solutions” come in.
Ultimately somewhere between an “educated guess” and JUGAAR!

24. Engineering Aerodynamic Softwares
For preliminary aircraft design, we need quick, somewhat crude solutions. Ball park estimates will do.
The USAF saw that need, and decided to compile data on aerodynamic predictions. Contract: McDonnel Douglas.
There were some approximate analytic solutions.
There were some correlations.
There were half a century of wind/water tunnel tests
All of this was compiled in two volumes called USAF Stability and Control Data Compendium (or DATCOM!) in 1978

25. What is DATCOM?
DATCOM is a collection, correlation, codification, and recording of best knowledge, opinion, and judgment in the area of aerodynamic stability and control prediction methods.
Used for
Conceptual and Preliminary aircraft design
Evaluate changes resulting from proposed engineering fixes
For making simulators.
For any given configuration and flight condition, a complete set of stability and control derivatives can be determined without resort to outside information.
Methods range from very simple and easily applied techniques to quite accurate and thorough procedures.
The book is intended to be used for preliminary design purposes before WT/CFD.
It is not easy to sift through two volumes of 3000 pages though!

26. Digital DATCOM
 USAF Stability and Control Digital DATCOM is a computer program that implements the methods contained in the USAF DATCOM.
First version in Implemented in FORTRAN IV.
It calculates the stability, control and dynamic derivative characteristics of fixed-wing aircraft.
It uses text based input and text based output.
Some GUIs have recently come out, but are not very stable.
The program was declassified around the year 2000.  

27. What can DATCOM do? Datcom requires two basic inputs It calculates:
Flight Conditions (Altitude, Speed, Re, M, Flow angles)
Aircraft Geometry (Wings, Tails, Fuselage dimensions etc)
Optionally propulsion data (jet/propeller can also be input)
It calculates:
Lift, Drag, Moments, Center of Pressure, Flow angle derivatives (stability derivatives)
Output can be for whole aircraft or components
CL 
CD 
Cm 
CN 
CA 
CLα 
Cmα 
CYβ 
Cnβ 
Clβ 

28. Let’s Begin with the Input File
Remember we are talking about FORTRAN, so data must be entered in the correct column.
FORTRAN uses Control Cards (objects) and Namelists (functions).
Namelists start with $ sign. They star after one space.
Inputs to namelists can be entered one space after a namelist title or beginning with the third space of a new line.
Control Cards come alone on a line. The start in the first column.
Easier to edit old files than making one from scratch.
Begin by first naming the aircraft or “case” to be run.
This is done by typing CASEID, spacing once, and typing the desired name.
CASEID is a control card, and thus the “C” should be the first letter on the line and no characters should follow the case name on the line.
Next, the system of units for the input may be specified by DIM control card :
DIM M – kilogram-meter-second
DIM CM – centimeter-gram-second
DIM FT – foot-pound-second
DIM IN – inch-pound-second
Angles are entered as degrees, always!

29. Next, flight conditions should be entered.
This is done by calling out the FLTCON namelist. A namelist must be called out on a new line by spacing once and entering the $ symbol followed by the namelist title. 
The inputs under the FLTCON namelist includes
MACH – Mach number
VINF – Airspeed in units of length (as chosen by the DIM control card) per unit time
NALPHA – number of angles of attack to be evaluated
ALSCHD – angles of attack to be evaluated, written sequentially
GAMMA – flight path angle
ALT – altitudes to be evaluated
WT – aircraft weight
Alternatively, Reynold Number can be entered.

30. What does it look like so far?
The “picture” so far

31. Geometry….Fuselage Next, geometry of the aircraft must be entered.
Fuselage is defined by the BODY namelist.
It can be defined by a maximum of 20 longitudinal stations.
NX – number of stations used to define the body
X(1) – longitudinal location of station
R(1) – planform half-width of the fuselage in the spanwise direction
ZU(1) – location of upper vertical surface of fuselage with respect to an arbitrary reference plane
ZL(1) – location of lower vertical surface of fuselage with respect to an arbitrary reference plane
Alternatively, a cylindrical fore, mid and aft body is all that is needed

32. Namelist BODY

33. Geometry….Lifting Surfaces
Wing, horizontal and vertical tails all have similar inputs.
Use  WGPLNF, VTPLNF, and HTPLNF namelists.
All the necessary inputs to define a straight tapered planform are as follows:
SSNPE – exposed semi-span
SSPN – theoretical semi-span
CHRDR – root chord
CHRDTP – tip chord
SAVSI – sweep angle
DHDADI – dihedral angle
TWISTA – twist angle
CHSTAT – reference chord station for inboard for panel sweep angle
TYPE – type of wing planform (1.0=straight tapered planform)
It is also possible to make cranked wings (see manual)

34. WGPLNF, VTPLNF, and HTPLNF

35. Wing Sections (Airfoils)
Airfoil can be entered using the NACA control card. (begin column 01)
NACA airfoil for a vertical tail is given by:
NACA-V
V specifies that the airfoil is for the vertical tail. A W, H, or F in the same place would specify the wing, horizontal tail, or ventral fin airfoil respectively.
The 5 specifies the type of airfoil, in this case the 5-digit airfoils.
Other options are 1, 4, 6, and S for 1-series, 4-digit, 6-series NACA airfoils, and supersonic airfoils respectively.
Last input is the airfoil designation.
You can also enter your own or exotic airfoils (See manual)

36. The “Picture” so far…

37. Locating the Components on the Fuse
SYNTHS namelist used to place wings, tail, center of gravity.
XCG – longitudinal location of center of gravity
ZCG – vertical location of center of gravity
XW – longitudinal location of theoretical wing apex
ZW – vertical location of theoretical wing apex
XH – longitudinal location of theoretical horizontal tail apex
ZH – vertical location of theoretical horizontal tail apex
XV – longitudinal location of theoretical vertical tail apex
ZV – vertical location of theoretical vertical tail apex
ALIW – wing incidence angle
ALIH – horizontal tail incidence angle

39. Reference Areas and Lengths
Finally, we may want to put our own reference areas and lengths (can be left if you want DATCOM to calculate the same)

40. Flaps, Control Surfaces
Flaps and elevators can be modeled using the SYMFLP and ailerons by ASYFLP namelists, which output results for symmetrical and asymmetrical flap deflections, respectively.
FTYPE – type of flaps (SYMFLP only)
NDELTA – number of flap deflections to be evaluated
DELTA(1) – flap deflections listed sequentially (maximum of 9, SYMFLP only)
CHRDFI – inboard flap chord length
CHRDFO – outboard flap chord length
SPANFI – spanwise location of flap inboard panel
SPANFO – spanwise location of flap outboard panel
STYPE – control surface type (1.0=flap spoiler, 2.0=plug spoiler, 3.0=spoiler-slot deflection, 4.0=plain flap aileron, 5.0=all moveable tail, ASYFLP only)
DELTAL(1) – left flap deflection angles listed sequentially (maximum of 9, ASYFLP only)
DELTAR(1) – right flap deflection angles

41. Control Surfaces

42. Some other Options
You may also want dynamic deratives (with pitch rate, angle of attack rate etc)
Use  DAMP control card 
DERIV RAD and DERIV DEG output these derivatives in radian and degree

43. Complete File

44. Processing the Input file
Save the file as ***.inp
Then run datcom.exe and process

45. Output Let’s see the output in Class.
You can import the ouput to Matlab using Aerospace Toolbox
alldata = datcomimport('astdatcom.out', true, 0);
Plotting Lift Curve Moments
h1 = figure;
for k=1:2
subplot(2,1,k)
plot(data.alpha,permute(data.cl(:,k,:),[1 3 2]))
end

46. Plotting the Input Aircraft
Bill Galbraith of HolyCows sells DATCOM+ for $100 doing this

47. Intermission – Equations of Motion

48. Equations of Motion So, these are 12 nonlinear ODEs.
There is no analytical solution.
We need to use numerical integration methods (Adams, RK..)
Luckily, this is all programmed in Simulink graphical programming language.

49. Simulink Aerospace Toolbox
Aerospace Blockset™ software extends Simulink® with blocks for
modeling and simulating
aircraft,
spacecraft,
rocket,
propulsion systems,
unmanned airborne vehicles.
aerospace standards,
modeling equations of motion
navigation,
gain scheduling,
visualization,
unit conversion

50. So, let us implement the first step

51. Next Set Some Aerodynamic Variables
Use conversions for flow angles (𝛼, 𝛽)
Use standard atmosphere and gravity models for (𝑔, 𝑀)

52. Tidy Things Up a bit
Create subsystems

53. A detailed example Lightweight Airplane Simulator Design
Four seater monoplane: Skyhogg
We will use Simulink for rapid
Aircraft design
Modeling
Simulation
Control Design

54. Aerodynamics The designed geometry is modeled in Datcom
Datcom provides aerodynamic stability and control derivatives and coefficients at specified flight conditions. 
Import in Matlab using
statdyn = datcomimport('SkyHogg.out');

55. Let’s get this Aerodynamics in Simulink

56. Next also put the Elevator Model

57. Equations of Motion Once again

58. Actuator and Sensor Models

59. Environmental Models

60. Trim and Linearize
Trim and Linearization can be done to find the operating point at specified speed and altitude, for example.
You Analysis>Control System Design> Linear Analysis

61. Linear System Analysis

62. Control System Design
Dual Loop Control
Time scale separation

63. Altitude Control

64. Pizzaz: Integration with FlighGear