# Simulating aircraft physics

1. May 21, 2010

### boks

I’m attempting to write an aircraft simulation game with believable physics, although it doesn’t have to be precise but I’m having a bit of trouble getting it off the ground so to speak.

When I plug numbers into the drag and rolling resistance formulas, I don’t think I get accurate results, so I must be doing something wrong along the way, as I’m by no means an expert at maths or physics. I’m not looking at lift just yet, but obviously I will at some point.
I’m sure I’m making plenty of silly mistakes, so please correct me where I go wrong. I’ve been attempting to get my head around this for a couple of days but I don’t seem to be making much progress.

For example, let’s take a Tornado GR4 with the following specs:
Weight: 13890kg
Thrust: 38.7kN
Wing area: 26.6m^2

Am I right in thinking I should be looking at rolling resistance rather than static friction in order to get the object (aircraft) moving along the ground?

Rolling resistance: F = C * Nf
Where F is the rolling resistance force
C is the rolling resistance coefficient
Nf is the normal force

Let’s take C to be 0.01 (ordinary car tyres on concrete).

Would the mass of the object be 13890 kg or 13890 / 9.81 = 1415.9 kg?
I’m a bit confused because force in Newtons has the units of kg ms^-2 but mass has the units of kg, although the units given for the weight (force), is in kg? If I were to take 1415.90 kg to be the mass, the normal force (Nf) would be 13890 N (1415.9 * 9.81)? I’m not sure that sounds right though :/

So the force required to get the object moving would have to be greater than 0.01 * 13890 = 138.9N?

For drag: D = Cd * A * 0.5 * r * V^2
Where D is the drag
Cd is the drag coefficient. Say 0.02
A is the reference area (for an aircraft, it’s the wing viewed from above which makes it easier/comparable to calculate the lift?). 26.6 m^2
r is the density of the air. 1.225 kg m^-3 (at sea level)
V is the velocity. Say 44 m^s-1
D = 0.02 * 26.6 * 0.5 * 1.225 * 44^2 = 630.8456 N

So how would I then calculate how much to slow the object down by? This is quite challenging for me as you can probably tell, but I hope to eventually grasp it. I’d appreciate any help that anyone is able to offer :)

Many thanks.

2. May 21, 2010

### PhanthomJay

Big problems when the specs list the weight of the aircraft in kilograms. 13890 kg is actually the mass. Weight = mg = 13890(9.8) Newtons. Max takeoff weight is 28000(9.8) N. Adjust rolling friction force accordingly (yes, it's rolling friction, not static or kinetic friction). Your drag formula is based on a certain speed...that should not be max takeoff speed, as drag is dependent on speed, which varies during takeoff...you'd have to use a weighted average speed, since calcs are a bit complex... I'm not sure what you mean by slowing down...F_net = ma, where F_net is the thrust less the friction less the drag.