General questions abou measuring aircrafts kn

[JRM]

Hi

 

I was wondering if theres a way to measure the kn of my current models (F18,F14,F16) Does anyone have a formula, im been trying with (N= KG x(Distance in meters/Time in seconds*2) this result I convert in Newtons but I get a unrealistic result with the F16 (325 kn) from traveling 40 km in 123 seconds.

 

SO I need a formula to caculate aircrafts KN, wikipedia says that F16 has 127,2 kn..how do they calculate that..I need this to finish th fm of some of my personal low fidelity projects

Edited September 11, 2020 by JRM

[=4c=Nikola]

That's easy. Gain access to the aircraft, bring large dynamometer, anchor it properly and measure.

 

Second question, formula for kn is n/1000

[Mumby]

I feel like I am going to get out of my depth pretty quickly here, but

 

KG * (distance / time*2)

 

has dimensions of momentum, not force.

 

I'm assuming that by kn, or KN, or N you are talking about the magnitude of the thrust? And that by KG you mean the mass of the aircraft?

 

If so, I think you might try measuring the acceleration of the jet and convert that to a force. Then make some assumptions about how the force varies with velocity, and how air resistance is going to increase with velocity.

 

Cheers

 

P

[Frederf]

You can only figure out the force of the engine by motion if there is no drag in the change of state path unless you know the drag characteristics. F = ma and so level constant speed flight is zero acceleration and consequently zero net force. Obviously the engine is producing thrust so why is net force zero? Because aerodynamic drag is equal and opposite.

 

A method which produces something like an answer would be to start the airplane at one speed and end at another. For example start at 0 speed on a runway and end at 100 knots. If that takes 10 seconds then there is 5.14 m/s^2 acceleration. Multiply acceleration by aircraft mass to get net force.

 

Net force will be the engine (forward) minus wheel drag and aero dynamic drag (backward) so you know your engine thrust is at least the number calculated above.

 

How do they do it in reality? They use a glorified bathroom scale while the engine is installed or uninstalled (test stand) and nothing is going anywhere.

[Northstar98]

Okay I'll have a stab at this.

 

Firstly, we need to know:

 

• The starting velocity of the aircraft in knots (preferably ground speed). (v)
  
• The final velocity of the aircraft in knots (again, preferably ground speed). (u)
  
• The total time between the measurements of initial velocity and final velocity. (t1)
  
• The fuel flow rate in pounds per hour (I'll do all the appropriate conversions), this needs to stay as constant as possible throughout ®.
  
• The initial aircraft mass in pounds (m1).
  

 

To do the test fly in a straight line, in 0 wind conditions, keeping a constant altitude, when you're ready move the throttle to maximum, wait for the fuel flow to stabilise (if possible) and measure the velocity. After a set time, record it again and note the time and fuel flow.

 

Finding the net force

 

Firstly we need to know the acceleration, we can do this with a simple kinematic equation; v = u + a*t, where a is acceleration, v is the final velocity, u is the initial velocity and t is the time between measuring u and v. We then rearrange to solve for a, which is a = (v-u)/t.

 

We then know that the net force (Fnet) = mass (m) * acceleration (a), we've worked out a, but the mass is changing so what we're going to need to do is integrate the mass differential (dm) with respect to time (t).

 

Assuming the fuel flow rate ® is constant, the equation for mass is going to be the initial mass - the fuel flow rate * time.

 

Differentiating the above with respect to time gives us dm = -r

 

So doing Fnet = a * the integral of dm with respect to time, between t = 0 and t = t1 gives us Fnet = a(m1 - r*t1).

 

 

Finding drag

 

Now as stated, Fnet is the net force on the aircraft, i.e the total thrust - the total drag. So what we need to do is work out the force of drag (Fd) and then add it to Fnet to find thrust (Ft).

 

So we'll also need to know the coefficient of drag for the aircraft (C_d), and its cross-sectional area (A).

 

Assuming C_d and A stays constant (both may vary based on surface deflections and AoA, but if we stay level these shouldn't be changing significantly, if at all).

 

The equation for Fd = 0.5 * ρ * v^2 * C_d * A where rho (ρ) is the fluid density (taken to be 1.2 kg/m^3, obviously though this will change with pressure and temperature, so knowing these 2 will be great, in any case it'll be assumed constant).

 

v is changing so we'll have to integrate d(F_d) in a similar fashion to above, so long as we know an equation for v, which we do, but we'll assume constant acceleration to keep things easy. As it's only v^2 that's changing we just need to integrate that over time, we'll call that dv2

 

The equation for v is v = u + a*t, therefore dv/dt is just a and the integral is a*t + c where c = u

 

The equation for v^2 = u^2 + 2*a*t + a^t*t^2, so dv2/dt = 2*a + 2*a^2*t

 

So now we do integration again between with respect to time between t = 0 and t = t1 and we get Fd = 0.5 * ρ * C_d * A * 2*u*a*t1 + a^2*t1^2 + c where c is u^2 (from above).

 

 

Putting it all together

 

Putting everything together and our equation for thrust = a(m1 - r*t1) + 0.5 * ρ * C_d * A * 2*u*a*t1 + a^2*t1^2 + u^2

 

 

I'm currently writing a python script to do all this for us, all we need to do is feed it the variables. Of course if anyone spots a mistake in my maths above feel free to correct me.

 

In real life though, engine performance is done on a test static test stand, pressing against what is essentially a set of scales - something that can measure the force directly.

Edited September 13, 2020 by Northstar98