Hurricane Mk IIC cannon:drum-magazine or belt-fed?

[Bill Walker]

A very interesting thread. Just one small observation: inertial coupling is a gyroscopic effect that impacts handling and control, not performance. It is most frequent in aircraft with very low roll inertia (like early small wing jet fighters), and shows up as unintended (and in the worst case uncontrollable) pitch and yaw in response to roll control inputs. Adding heavier guns in the wings would actually reduce this effect.

[Johnny .45]

Yeah, that sounds right. As far as I knew, inertia coupling is an effect of very high speeds and small wingspan. I don't think the Spitfire ever suffered anything quite that extreme...it was laterally unstable and hard to fly in a straight line, but inertia coupling is a potentially deadly effect. I'd think something more like "Dutch roll" would be the case. If it ever got fast enough to be susceptible to inertia coupling, it would have been in a very fast dive, not level flight.
So I can't say which is correct, and I'm curious to find out.
As for the cannons helping stability...I'm dubious. Maybe by adding a little inertia to dampen things a bit, but inertia has it's opposite, momentum.

[Bill Walker]

Originally Posted by Johnny .45

As for the cannons helping stability...I'm dubious. Maybe by adding a little inertia to dampen things a bit, but inertia has it's opposite, momentum.

I only meant that they would help reduce any inertia coupling.

Dutch roll is present in all flying machines to some extent, and results from the fact that control surfaces will always produce some slight effect in all three axes, even if intended for primarily one axis. It can happen at very low speeds. I've seen it occur in helicopters at 100 knots. Mass distribution will have very little effect on this. Span wise mass distribution can effect roll rate, and has a very pronounced effect on the rate of change of roll rate in response to a control input. Cannon in the wings may slightly increase the maximum roll rate (P), but will have a much more noticeable effect of decreasing the rate of increase of roll rate (P dot) after a given control input. This could be very upsetting to a pilot in air-to-air combat.

All very hard to put in words. A graph would be much easier .

[Johnny .45]

Okay, I think I mostly follow you here..."mass distribution", i.e. how far apart the weight is along the wingspan. The more weight you have out in the wings, it will effect roll rate...we had this discussion on a different site regarding the P-38. The way I read it was that the P-38 was a quick enough roller, but it's RESPONSE to the control input was slow...with those heavy engines out on the wings, it took a moment for it to "accelerate" into it's full roll rate. Like a heavy car can have the same top speed as a lighter car, but for the same power, the lighter one will be far quicker "off the line".
Cannon would have a similar effect...between a .303 and a 20mm-armed Hurricane: the wingspan is the same, the ailerons are the same, so the force the ailerons produce is the same, only it's trying to move a much heavier cannon. Friction isn't an issue, so the only effect is that it builds up roll-speed slower.
But part of what I was saying is if a pilot has to use slight OPPOSITE deflection to STOP the roll (the momentum will try to keep the roll going), it will be all the more sluggish on STOPPING the roll. Like the lighter car can out-accelerate the heavy car, it can also stop quicker too. Momentum and inertia involve exactly equal forces...there IS no difference, in terms of physics. An object in space doesn't "know" it's moving; in fact, I think it's aeronautical-engineering lingo to call momentum "reverse acceleration".
But I don't see how cannons could INCREASE the maximum roll rate. The maximum rate would be the same, it would just take longer to build up to that rate (and longer to stop). If heavy cannons increased any performance parameter, it'd be dive-rate! A little extra weight to increase the terminal velocity...although I'm not sure whether in that situation more weight would make a lot of difference, or if it's more about the power of the engine.
I'm curious about that now, too! If a plane can dive at 500mph at full power, how much slower would it be in a glide? The Thunderbolts impressive diving ability makes me suspect that the weight of the plane is important, and I'm not even sure if a prop on full power at 500mph is helping to propell the plane, or if it's just contributing to drag at that point!
Anyway, I guess we can chalk "roll-response rate" up as one potential advantage of a fuselage-gunned fighter over a wing-gunned fighter. All other things being equal (using the same plane, etc.), a Bf 109G with wing guns fitted would be slower into a roll than a Bf 109G withOUT wing guns. Of course, we (mostly) all have heard of how the Bf 109 "Kanoneboote" was disadvantaged by it's wing guns, so now we know why. Although, of course the projecting underwing gondolas would create a little drag, too.

[Bill Walker]

Originally Posted by Johnny .45

Okay, I think I mostly follow you here..."mass distribution", i.e. how far apart the weight is along the wingspan.

Correct.

...with those heavy engines out on the wings, it took a moment for it to "accelerate" into it's full roll rate. Like a heavy car can have the same top speed as a lighter car, but for the same power, the lighter one will be far quicker "off the line".

Exactly. "P dot" is defined as the rate of change of roll rate with time. Think of the units: degrees per second per second

Cannon would have a similar effect...between a .303 and a 20mm-armed Hurricane: the wingspan is the same, the ailerons are the same, so the force the ailerons produce is the same, only it's trying to move a much heavier cannon.

Yup.

But part of what I was saying is if a pilot has to use slight OPPOSITE deflection to STOP the roll (the momentum will try to keep the roll going), it will be all the more sluggish on STOPPING the roll.

Today an airplane designer calls all this "agility", or the ability to point where you want, when you want, both accurately and quickly. It is a combination of speed of control response (both control input coming on and coming off), sustained rates (pitch, yaw and roll), and repeatability.

But I don't see how cannons could INCREASE the maximum roll rate. The maximum rate would be the same, it would just take longer to build up to that rate (and longer to stop).

The increased inertia can over power the ability to stop or even reduce the rate of roll. Some high speed aircraft have very strict restrictions on roll rate with wing stores, as the pilot soon looses the ability to stop the increasing roll rate, until things start breaking and falling off. Usually this is not desirable.

If heavy cannons increased any performance parameter, it'd be dive-rate! A little extra weight to increase the terminal velocity...although I'm not sure whether in that situation more weight would make a lot of difference, or if it's more about the power of the engine.

Terminal velocity occurs when accelerating down forces (gravity plus thrust) equals drag. Extra weight, anywhere, can increase terminal velocity. However, for most modern combat aircraft, and even for some slippery WW2 fighters, this classic definition of terminal velocity doesn't really mean anything. Drag is so low that very high speeds are needed to get drag up to equalling weight. Some other limit will be reached first: structural, aeroelasticity, etc. Today most fighters would start to melt, or just run out of altitude, long before terminal velocity is reached.

If a plane can dive at 500mph at full power, how much slower would it be in a glide? The Thunderbolts impressive diving ability makes me suspect that the weight of the plane is important, and I'm not even sure if a prop on full power at 500mph is helping to propel the plane, or if it's just contributing to drag at that point!

Propeller efficiency, and therefore thrust, does decrease as forward speed increases, but I suspect that a constant speed prop would break off long before it even produced zero net thrust. You can produce braking by operating at non-ideal blade angles - reverse thrust as often used on short landings by C-130s and others.

And anyway, speed is not primarily a function of engine throttle setting, but more a function of wing angle of attack. Throttle setting will mostly determine if you are climbing, level or descending at a given speed. The speed, within normal operating limits, is determined by elevator control position and pitch trim setting (if the airplane has this). That is why flying an airplane has been described as rubbing your stomach and patting your head at the same time.

[Johnny .45]

Originally Posted by Bill Walker

Correct.

Exactly. "P dot" is defined as the rate of change of roll rate with time. Think of the units: degrees per second per second



The increased inertia can over power the ability to stop or even reduce the rate of roll. Some high speed aircraft have very strict restrictions on roll rate with wing stores, as the pilot soon looses the ability to stop the increasing roll rate, until things start breaking and falling off. Usually this is not desirable.


Propeller efficiency, and therefore thrust, does decrease as forward speed increases, but I suspect that a constant speed prop would break off long before it even produced zero net thrust. You can produce braking by operating at non-ideal blade angles - reverse thrust as often used on short landings by C-130s and others.

And anyway, speed is not primarily a function of engine throttle setting, but more a function of wing angle of attack. Throttle setting will mostly determine if you are climbing, level or descending at a given speed. The speed, within normal operating limits, is determined by elevator control position and pitch trim setting (if the airplane has this). That is why flying an airplane has been described as rubbing your stomach and patting your head at the same time.

So what is the definition of "P dot"? I mean, what does it stand for? I can never remember all the jargon, but it's like "Vmax" is the maximum safe speed for whatever operating conditions apply..."Vmax = Velocity Max".
So is the "dot" supposed to be like a decimal or period? Or is it "d-o-t", and the letters stand for something?

And what I was saying about the cannons effect on "P dot"...your first post said:

"Cannon in the wings may slightly increase the maximum roll rate (P)"

...did you really mean to type "decrease"? Because in the next post, you say:

"The increased inertia can over power the ability to stop or even reduce the rate of roll. Some high speed aircraft have very strict restrictions on roll rate with wing stores, as the pilot soon looses the ability to stop the increasing roll rate, until things start breaking and falling off. Usually this is not desirable."

The second makes more sense to me...I just don't see heavy cannons actually INCREASING rate of roll...they'd just make it a lot harder to STOP the roll, wouldn't they? It's funny how even a little weight in the wrong spot can alter an aircraft's handling so much!
What you said about "speed is not primarily a function of engine throttle setting"...that's less true with a powerful combat plane than with a small, docile plane, isn't it? With old biplanes, you climbed by increasing the throttle, and descended by lowering it. But with a warbird, anything over cruising speed is only maintained by high power levels...the second you "let off the gas" it begins to slow down until the drag matches the lower power setting. You CAN maintain speed, by only by loosing altitude. So I can't say that what you said is WRONG, because it's not...but the throttle did have other uses, or at least it was bit more complex than flying a Stearman!
I remember reading somewhere that a pilot could use the throttle to slow himself down and avoid overshooting...the prop acts as an airbrake, and early jet-fighter pilots had trouble adapting to the fact that they couldn't slow down and keep the sights on a target at the same time. You could nose up and slow down, but you wouldn't be able to shoot at the same time.
Of course, that was quite a while ago that I read that...it may be that the guy was referring to the fact that a Me 262 pilot couldn't "chop" his throttles, or he'd flame out the engines. In a prop fighter, even cutting the power while at high speeds will make you slow down quickly, but an Me 262 couldn't do that, and without an airbrake, he was stuck at the speed and power of the engine.
Interesting stuff; it makes me think! Thanks.

[Bill Walker]

P is rate of roll. Say degrees per second. Anything "dot" to an engineer is rate of change with time. So, P dot (usually written as the letter P with a dot over it, but I can't figure out how to do that here) is degrees per second, per second. If you start with a roll rate of zero, and one second later your roll rate is 90 degrees per second, your average P dot over that one second was 90 degrees per second, per second.

In most aircraft, a roll input (aileron deflection) induces mostly a P dot. I'm using a lot of weasel words here, like "mostly", because I'm over simplifiying. Partly because it's hard to put equations in words, and partly because I've forgotten a lot of stuff. So, with cannon in the wings, P dot initially may be slow to build (because of roll inertia) but it will build. It then becomes hard to stop, again because of inertia. Moving the stick the other way introduces a P dot of a different sign (roll rate starts to decrease, but is still positive for some time). It takes you longer to reduce and then reverse P dot, so P continues to build. That's why you see modern aircraft with restrictions on roll inputs with wing stores or tip tanks. It will get away from you. You will reach a dangerous value of P even after you have reversed the stick.

The short term response to a throttle increase may include a speed increase, but the long term response will always be an increase in climb rate. Modern aircraft have to be designed to minimize the short term response. It's built into the regs a designer has to meet today, but this has not always been the case. But the long term response is built into the laws of physics. Different aircraft may have different short term responses, but the long term response will ALWAYS be the same. This is all complicated when the power change changes the aircraft trim state (due to thrust vector not being aligned with the drag vector). This will be more noticeable in a higher powered aircraft. Then, a throttle input is also partly a longitudinal trim input, and longitudinal trim "mostly" controls speed. But still, the throttle "mostly" controls rate of climb. Notice the weasel word again? What this means is that it is not a case of the pilot "can maintain speed by loosing altitude". The aircraft WILL maintain speed by loosing altitude, unless the pilot does something in the pitch plane.