Mon Apr 01, 2002 4:11 am

Just a couple of more thoughts to add....

Let's get back to first principles and do a little sanity check.... FredT and others gave a good "formula" for thrust / velocity, but here is the "rest of the story":

Newton's famous second law actually states that force is equal to the "rate of change of momentum". The familiar F=ma is only a special case of this.

Momentum = m.v (mass x velocity)

Rate of change of momentum = d/dt (m.v)

= v.dm/dt + m.dv/dt

(you need to know a bit of calculus to follow the above step)

In words, force is equal to mass flow rate (dm/dt) times velocity plus mass times acceleration (dv/dt). The second part, m.dv/dt = m.a (mass times acceleration) is the familiar form of Newton but is only true if there is no mass flow component.

Now, is 200 mph air velocity reasonable? Consider a control volume enclosing a moving aircraft at a single instant of time. The air in front of the a/c is at rest. The air behind the a/c is moving at 200 mph. The force exerted on the control volume is v.dm/dt, where v is 200 mph and dm/dt is mass flow. What is the mass airflow required to generate 60,000 lb thrust?

dm/dt = F/v = 60,000 lbf/293.3 ft/s = 204.8 lbf-s/ft

I use lbf to indicate pounds-force units. To get it into pounds-mass, multiply by g = 32.2 ft/s^2. This yields

dm/dt = 6595 lbm/s.

Is this reasonable for a large engine?

Actually, no. For a JT9D engine, the velocity behind the fan is 885 ft/s, while out of the turbine it is 1190 ft/s. This is at sea level, static conditions, at 43,500 lb thrust. The mass flows are 1248 lb/s at the fan, and 247 lb/s at the turbine.

What about pressure? It doesn't really matter! Velocity and pressure are related by the Bernouli equation: P = 0.5 rho.v^2, where rho is air density. If you take the air at 200 mph velocity and stick a wall behind it to make it stop, you will get a pressure rise according to half-rho-v-squared. If you integrate this pressure over a large area behind the a/c, you will get the same 60,000 pounds as you get with Newton. That's the beauty of physics -- everything is related, and there are many ways to get to the same result.

Cheers,

Pete

"In God we trust, everyone else bring data"