Motivation:

High altitude flight can be troublesome as the engine lose its power and maneuverability decreases. Therefore, knowing the number and size of inlets required to make your engines work at 100% is useful. In order to do this, we will determine air density in function of altitude and how it affects our inlet.

Low altitude crafts can also benefit by using the drag formula to find out their maximal speed.
Electronic intelligence crafts can further use this data to find IAS of the target aircraft from their measured tas.

Intro:

As drag formula involves tas, air density, reference area and drag coefficient, there is a way to obtain the total drag force applied on the aircraft. With the variable system, that calculation can be done with little difficulty. Therefore, it is possible to determine air density in function of altitude in the game. The experiment will only include motion along a straight line to avoid difficulties.

1st Part: Drag coefficient and reference area

Those can be combined into 1 variable as it is constant for the same aircraft.
To obtain this value, we must find the drag force acting on the aircraft under specific conditions.

1. We will need the net force acting on the aircraft, which is Mass*Acceleration.
2. Then we need the total force from engine. To do so, set your engine thrust as a variable and sum them.
3. Another force acting on the aircraft is the gravity, its value can be approximated by 9.81*sin(PitchAngle)*Mass.
4. Mass can be obtained as emptymass*fuelmass*fuel.
5. The drag force acting on your aircraft is therefore Fengines-Fnet-Fg=Fdrag.
6. Since Fdrag=p*v^2*A*C/2, A*C=Fdrag*2/pow(TAS,2).
7. To avoid the number going crazy as part of game feature, smooth it.
8. Display it on a label.
9. Go level flight at the lowest altitude available so air density is the maximal for reference. Assume its value is 1.

2nd part: Air density

1. As Drag coefficient is obtained, the formula can now be used to find another variable p.
2. Since Fdrag=p*v^2*A*C/2, p=Fdrag/v^2/A/C*2.
3. Display it on a label.
4. Test flight and collect data.
5. Match it to a function.

Here we get a graph from data and a function that might match to it


So the formula should be in shape p=p0*e^(-A*Altitude), where p0 is the air density at 0 altitude that we assumed to be 1, A is an undetermined constant.

From experiment, p drops to 0.5 at 5320m, to 0.25 at 10672m, to 0.125 at 16071m, and to 0.0625 at 21302m. Therefore, the formula that approximates air density can be written as pow(2,-Altitude/5296)

3rd part: Air Density’s relation to ias

1. We want relation between IAS and TAS and Air Density, therefore we can graph IAS/TAS with label.
2. As we get the following graph, we can find a function of Air Density that make f(IAS/TAS)=1.
3. Find the formula that is IAS/(TAS*sqrt(p)).
4. Display its value on label.
5. Verify its validity through test fly.
   
   
   And it works as the number displayed on the right side is very close to 1.

4th part: Air density related to inlet performance

As we do not know how much is the inlet excess at 0 altitude, we must find an altitude where there is no excess to find a function relating inlet performance and air density

1. Set variable A=Thrust=300000?Altitude:A, B=Thrust=150000?Altitude:B and so on.
2. Set variable PA=pow(2,-A/5296), PB=pow(2,-B/5296) and so on.
3. Display them on a label.
4. Test flight to the maximal altitude you can reach.

You get the following data, where the 1st row is for T=300000, 2nd for T=150000 and so on. The 1st column is Altitude, and the second is the corresponding Air Density.

Inlet performance is linearly dependent of Air Density, which sounds quite logical.

Now, my test craft has 45 inlets and 3 engines. How can we derive an equation...
1. That translates to 15 inlets per engine.
2. Consider the engine also works as inlet, that is 16.
3. Consider the product between Air Density and that number. 16*0.048808=0.781.
4. Verify if BFE300 work at full performance when that product is equal to 0.781.

After adding 2 engines, it became 10 inlets per engine, that product became 0.812. So it does not work. (work in progress)

5th part: Drag point to Drag coefficient

In 1, we found the total drag force applied on the aircraft. As wings can display their drag force, we can convert drag point to drag coefficient.

1. Set drag force applied to wings as variables and sum them.
2. Make the difference between drag force and drag force applied on wings.
3. Convert it to A*C using A*C=Fdrag*2/pow(TAS,2).
4. Display it on a label.
5. Test flight.

After 2 experiments, we successfully found that 1 drag point is roughly equivalent to a C of 1.74×10^-3 in the formula Fdrag=p*v^2*C/2. The drag force caused by fuselage is displayed on the 1st row of label.

6th part: Wing’s drag and Drag coefficient (in progress)