[Harri Pihl]

Originally Posted by drgondog

First- at Vmax the Thrust Hp is maximum for that altitude and weight.

I don't actually calculate the thrust hp but directly the thrust from the brake hp; the hp chart I used just gives the bhp.

Originally Posted by drgondog

When weight increases, for the same airframe, the Thrust Hp remains the same, but Vmax decreases alightly as the AoA must increase to maintain level flight for that Thp and weight condition.

The thrust remains same at original velocity but at the new balance point at lower speed the thrust will be higher.

Originally Posted by drgondog

If you want to demonstrate the math that proves a slight increase in AoA from freestream impingement on the propeller plane increases the change in momentum of the mass flow through that plane (positively) - give it your best shot.

Ok, I'll demonstrate using the calculation I did for the P-51B:

First thrust at original 9680lbs (4390,85kg) and 352mph (566,368km/h=157,3244 m/s):

1580hp = 1178014 W
exhaust thrust = 120kp = 1176,798N
Propeller Thrust = (0,8*W)/V = 5991,216N
Combined thrust = 7168,014 N

Then thrust at 10280lbs (4663,008kg) and 351mph (564,887km/h=156,913m/s)

1580hp = 1178014 W
exhaust thrust = 120kp = 1176,798N
Propeller Thrust = (0,8*W)/V = 6006,923N
Combined thrust = 7183,721N

Now we know that at the supposed new balance point there is 15,7N more thrust available so lets check if the D = T at these points:

First at 9680lbs

Speed =157,324m/s
density = 1,225kg/m3
wing area = 21,83m2
Aspect ratio = 5,83
Lift = 4390,85*9,81 = 43059,51 N
Calculated Cd0 = 0,020504
e = 0,8

Cl = L / (A * 0,5 * r * V^2) = 0,130111
Cdi = Cl^2 / (pii * AR * e) = 0,001156
Cd = Cd0 + Cdi = 0,021659

D = Cd * r * V^2 * 0,5 * A = 7168,014N = T Check!

Then at 10280lbs

Speed =156,913m/s
density = 1,225kg/m3
wing area = 21,83m2
Aspect ratio = 5,83
Lift = 4663,008*9,81 = 45728,487 N
Calculated Cd0 = 0,020504
e = 0,8

Cl = L / (A * 0,5 * r * V^2) = 0,1389007
Cdi = Cl^2 / (pii * AR * e) = 0,0013171
Cd = Cd0 + Cdi = 0,0218206

D = Cd * r * V^2 * 0,5 * A = 7183,721N = T Check!

Q.E.D.

Originally Posted by drgondog

Your specific references for each claim you just made for the P-51B?

It's calculated backwards from the linked chart:

http://www.wwiiaircraftperformance.o...level-blue.jpg

And using something else does not make a big difference, ballpark should be correct. The point here is to show the principles.

Originally Posted by drgondog

For example "e" is derived empirically, because the effect of spanwise lift distribution, increase in trim drag and the increases in all forms of drag on the airframe. .8 is a good rule of thumb for conservative preliminary design purposes - but only that unless you have test results?

It's just an estimate. I can calculate e from various data but 0,8 should be a good enough estimate.

Originally Posted by drgondog

Ditto prop efficiency. .8 to .85 are good Prelim Design numers. So where would point me to .8 as being correct for the P-51B?..

Same here, just an estimate. I have the Hamilton standard red book so I can make a better estimate but again 80% should be good enough for the purpose.

Originally Posted by drgondog

Having said that, how do you arrive at approximately 1mph delta for a 6% weight increase? What math are you using?

I have listed the formulas on the page 5 of this thread and Chapter 14 of Hoerner's "Fluid Dynamic Drag" shows an example.

Basicly we don't know the Cl, drag, thrust nor speed at new balance point. However, we know how each of these behaves so we can solve the problem with iteration process. If you look the above calculation, you can see that it really works.

I can put together a small spreadsheet to demonstrate the calculation if you are interested; you can change the parameters and see the results instantly. My stuff is written in Finnish so translating might take some time.