Calculated roll rates

[F4UDOA]

Pb/2V is the helix angle at the wingtip in radians.

Could somebody please explain Pb/2V? I have been down this road a hundred times and I just can't get it.

Here is an example that was drawn for me by someone else.

In the case of the P-47, this angle was 0.074 * 180 / PI = 4.24 degrees
Then roll rate will vary in direct proportion to wingspan and forward velocity.
In the P-47's case, with a 41' wingspan, the tip must travel a distance of PI * 41' = 128.8' in one roll.
tan(4.24) * forward velocity = roll velocity
for 200 mph (293.3 ft/sec)
roll velcity = 21.75 ft/sec
time to roll = 128.8 ft / 21.75 ft/sec = 5.92s

Questions
1. How do you know what the helix angle is? Is is constant or variable?
2. How does hydrolic boost modify this equation?
3. "tan(4.24) * forward velocity = roll velocity" Then it shows the roll velocity of 21.75FPS. How? not according to my math?
   
Any ideas?

[hitech]

F4UDOA:

Given no limiting factors a planes roll rate is like a screw threw the air. If you picture the plane a nut on a bolt you can see whats happening.

If you move the nut forward on the bolt slowly, it will spin slowly.

If you move the nut fast it will spin fast, But the nuts spin's per dist always remain constant.


This is what is described by the equation you are using.

So to compute that term you basicly just have to look at slower speed roll rates, I.E. speeds where the roll rate varies linarly with speed.

As to bosted ailarons, it dosn't effect that equeation. What boost does is effect the rates above where the linar roll rate could be used pryor to the boost.

HiTech

[niklas]

Hmmm...  the most significant influence that stops the linear roll rate increase is wing twist and aileron elasticity. Boosted ailerons won´t help here too. Depending on where the booster is located they may help to avoid elasticity of the control system though.

The twin boom design of the P38 maybe stiffened the wing during a roll. Because the wings are twisted in opposite way the connection by the elevator countered probably the twist. Maybe this was one the reason for the linear increase of the rollrate up to pretty high speeds in case of the P38.

Furhtermore all elevator forces are led into the inner wing part by the two fuselage parts of the P38. This means the inner wing part must have been pretty stiff against twist, because the momentum due to the long distance elevator-wing  is very high. The resulting momentums of the elevator were maybe much higher than these of the ailerons. So the inner wing part of the P-38 must have been very very stiff against twist, a natural requirement of such a twin boom design imo. That means that the reminding outer section of the wing was the only part that could be significantly twisted by the ailerons, and this section is comparable or even smaller than a wing side of a single engine design. All together it explains very much why the P-38 roll rate increases linear up to high speeds.

On the other hand it would be interesting to know hoch much elevator forces twisted the wing and influenced thus lift and flight characteristics in case of the P-38

niklas

[Angus]

So what is the benefit of boosting ailerons?

I'd say that it is the application of inhuman force of a control surface.

And it works. Probably with some extra drag penalty though.

[gwshaw]

Originally posted by Angus
So what is the benefit of boosting ailerons?

I'd say that it is the application of inhuman force of a control surface.

And it works. Probably with some extra drag penalty though.

When airspeed and Q is high, control forces go up. Boosting keeps control forces more or less constant. At a speed where other planes may require 50 lbs stick force for 1/4 aileron throw, the P-38 stick force is more or less the same as it was at 100 IAS.

There would be no additional drag other than some induced drag from the aileron movement. But that would be the same as non-boosted plane with the same ailerons.

Greg Shaw

[F4UDOA]

So what is the helix angle exactly?

What does it represent? The near 6 second roll number at 200MPH for the Thunderbolt is a very close to an accurate figure. Is this number unique to the P-47 or would I find the same result for the P-38 or C-47? If I were to compare the FW190 and F4U would they be the same or different?

I was just reading the Joint Fighter Conferance notes and they were discussing the Pb/2V of the P-51.

Is this generic or does it have some merit to distinguish aircraft types?

[F4UDOA]

GwShaw,

I noticed you posted on another message board some performance stats of the F4U-4 that you listed at two different weights. One full fuel and one 60%. Do you have the originals or did you see these listed somewhere else?

I have never been able to find the source for these numbers I have seen posted elsewhere.

[gripen]

Originally posted by F4UDOA
So what is the helix angle exactly?

What does it represent? The near 6 second roll number at 200MPH for the Thunderbolt is a very close to an accurate figure. Is this number unique to the P-47 or would I find the same result for the P-38 or C-47? If I were to compare the FW190 and F4U would they be the same or different?

I was just reading the Joint Fighter Conferance notes and they were discussing the Pb/2V of the P-51.

Is this generic or does it have some merit to distinguish aircraft types?

The main point for using the helix angle as standard is that  results are comparable in some degree regardless the speed and the altitude the measurement is made. However you can't directly compare roll rates with the Pb/2V values of the planes with different span because Pb/V2 values are based on wing span. Just think the AoA of the propeller at the root and the tip, for same roll rate (deg/s) at given speed a plane with shorter span should have a higher helix angle than a plane with longer span.

gripen

edit: Oops... My mistake: For given roll rate (deg/s) a longer span wing should have higher helix angle than shorter span wing; I thought propeller example wrong way.