Performance of the Fw 190A on the Deck?

[drgondog]

Originally Posted by Franek Grabowski

Bill, it is obvious that P-51B/C was aerodynamically slightly different than D/K. I cannot say for sure, but I suppose there might have been some other slight differrencies, eg. in props.

Forgot to answer this in detail. The external differences were to remove turtledeck, change the slope of the windscreen, add the bubble canopy, increase the Root chord to five a steeper angle of the inboard wing to fuselage.

Internal differences, Uplocks for wheels, increased thickness of ammo doors and add 2x .50's plus 660 rounds of ammo, and beef up the vertical stabilzer spar/fuse attach structure..slight change in horizontal stabilizer incidence

Props same except K had a slightly different prop, only to extent of removing sleeve at propeller hub. Same wing except as noted above

Later the D got metal elevators, tail strake.

Net - 51D cleaner, heavier, slower than P-51B-15 with same prop and engine in both airframes - about 10-12 mph on a statistical average via flight tests at Wright Pat and Eglin and NAA facilities.

[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.

[Franek Grabowski]

Bill
There must have been some differrencies in aerodynamics, because P-51D turned highly unstable at high speeds and had to be modified. That is one thing.
Another is accuracy of such calculations. As we know, engineering theories are based on approximates and simplified theories, and quite often we do not know what is actually going on. This is very important in understanding calculations of performance.
If methods widely used give us 10% accuracy (~40 mph!), and the result must be verified in tests of actual aircraft, which then has some not insignificant margin for quality of production, then we find that those few miles are just unmeasurable. On the other hand, we know that horizontal speed is just resulting from several factors. The most important is the airfoil used, then wing, then airframe, then engine and prop. Given each factor's share, it was concluded that small changes of weight are just unimportant in overall picture. That is what Graham is trying to show all the time.
BTW
Spitfire IX and Mustang III/IV/IVA were powered by the same Merlin engine. Which one was heavier and which one was faster?

[Crumpp]

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.

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

Hairi Pihl says:
Then at constant power the thrust increase when the speed decrease because:

T = (n*W) / V

Where n is efficiency and W is engine power.

Actually you do calculate THP. You just don't seem to understand completely exactly what you are parroting.

All the best

Crumpp

[Crumpp]

There must have been some differrencies in aerodynamics, because P-51D turned highly unstable at high speeds and had to be modified. That is one thing.

The designs had different stability and control issues. Bill is correct in his assessment however.




All the best,

Crumpp

[Franek Grabowski]

OK, so what is the point in underlining some of those figures? How about wetted area and the method it was calculated in each case? How about different AoAs or Res? Could you explain to us what is scientific value of the table while discussing aerodynamical characteristics of P-51?

[Crumpp]

OK, so what is the point in underlining some of those figures?

To make it easier for you to find the values measured by different agencies and test facilities that where equal. It was just a courtesy, Franek. It was not meant to offend you.

You are welcome to the entire report. It was given at an AIAA conference and is a very interesting read exclusively on the P51 series.

PM me if you would like a copy and it details the methods of measurement.

All the best,

Crumpp

[Harri Pihl]

Originally Posted by Crumpp

Actually you do calculate THP. You just don't seem to understand completely exactly what you are parroting.

If you care to read the part you quoted, the power unit BHP is allready converted to the Watts (SI unit) at that stage and then directly calculated to the corresponding amount of thrust, Newtons in SI units.

And as a friendly advice (again); Please leave that agressive attitude to the another forums.

[Crumpp]

If you care to read the part you quoted, the power unit BHP is allready converted to the Watts (SI unit) at that stage and then directly calculated to the corresponding amount of thrust, Newtons in SI units.

And as a friendly advice (again); Please leave that agressive attitude to the another forums.

Which makes no difference whatsoever. You are still using Thrust Horsepower. There is nothing aggressive in the facts.

[Harri Pihl]

Originally Posted by Crumpp

Which makes no difference whatsoever. You are still using Thrust Horsepower. There is nothing aggressive in the facts.

If you want to see the thrust horsepower in the calculation, just convert the power value back to bhp and multiply with n. However, I don't see any point to do that because, after initial conversions, the entire calculation is done with SI units.

And continous use of harsh words and continous claims that I don't understand what I'm doing, are indeed agressive actions.