thrust for max bank / g's

[MikeSt]

Assuming that the aiframe can take the stress, what is the rule of thumb / (or better yet the formula), to calculate the thrust needed for a max bank ... say 89.9 degrees ?

I found a formula to calc the stall speed at various bank angles.

Vsb = Vs / sqrt(cos(bank))

Using a Vs of 10 mph, the formula yields a Vsb(83deg) of around 30 mph which sounds reasonable.

Vsb(89.9) gives around 240 mph !

Is that correct? .. never mind the difficulty of flying that bank angle ;)

But it's not just a matter of having enough thrust / power to achieve 30mph in level flight is it ????

Btw my interest in this stems from playing with the Falcon4 simulator (F16 simulator).

The very detailed manual talks about the "corner speed" of an aircraft, which for the F16 is around 330 knots.

With a stall speed of around 170 mph, the previous formula yields a stall speed of around 509 mph at ~83deg bank (9g limit).

Since the corner speed is much less than the calculated stall speed, I'm assuming that the excess thrust effectively reduces the stall speed somehow ????


Another one of my questions that might not have much practical use, but I'm sure one or more of you guys can satisfy my curousity :)

Mike

[Eddie P]

Hi Mike-

You are on to the essence of what pilots call "flying the wing." Most accomplished pilots and RC flyers know this well. I'll try to throw a few ideas at you, but I'm not going to try to give the definative reply as that is only found in several full length books.

"Corner Speed" is an aerodynamic speed for each individual airplane design, where the tightest turn radius can be achieved. It is not a speed where you will be able to maintain altitude at an 89.9 degree bank. These two things are different.

First, an aircraft will turn based on the "horizontal component of lift" produced by the bank. At 60 degrees of bank, in level flight, a wing will produce a turn (a lateral acceleration in physics terms) at a rate of 2 g's, or twice the static gravity value. As you stated, you see the relationship of stall speed to the amount of g's you pull. When you pull g's, your stall speed goes up, and you can stall at a quite high yet predictable value, called an "accelerated stall". As bank increases, g"s and stall speed start to rise very quickly, in fact, expodentially. This is why your flight simulator F-16 manual tells you that you are limited to 83 degrees of bank, 9 g's, and 509 knots. We know fighters turn at all sorts of bank angles though, so see this as a level flight, 2 dimentional limit.

Corner speed is based on aircraft configuration, weight and design. It is a speed that the wing will be able to extract as much lift as possible to provide the lateral acceleration to turn tightly. However, it is also a speed that is not too high as to increase the amount of distance it takes to turn - as this would increase the overall turning radius and be counterproducticve.

Keep in mind a 90 degree bank is often thought of as a bank while maintaining level flight. In the real 3D world, when you bank an airplane 90 degrees, you are not always going to be going up against the hard core stall speeds and g's assiciated with the calculated values you were looking at. That's because these book values are looking at a 90 degree bank while maintaining altitude in a level plain.

If you go from straight and level and turn 90 degrees, and only pull back enough to cause, say, 2 g's to be pulled, your stall speed will only rise slightly. You will begin a descent, yes. But your airplane only knows the angle of attack the wing is seeing to the relative airflow you are flying through.

This is why in real airplanes, where equipped, pilots use an angle of attack guage (AOA guage) to measure the aircrafts energy state. If a turn needs to be made, bank the airplane 90 degrees, pull back and ride the AOA guage to extract the wings energy but don't go too far into the "stall" regime. A wing will always stall at the same angle of attack. It's the "critical angle of attack," so stall speed in terms of bank angle is better left to the guys on the ground with the calculators, while fighter pilots fly the AOA guage in the high stakes chess game of air combat. An advanced flight display will also show the stall speed as a red radial on an airspeed "tape" or similar, and the red radial will move as "g" loading changes. On the other side of the coin, if you are at zero g's, what do you think your stall speed is? It's zero.

The last portion of this is the energy required. You'll need a lot of thrust in order to maintain your energy state at the same altitude, or you will just kill your speed, and ability to turn, if unprudent cranking and banking goes on without respect to energy state.

You can crank and bank on modest power, however, if you use the "potential energy" of altitude, to trade for airspeed as your maneuvering occurs. This leads to the 3D thinking that if you want to turn tightly, for example, while at speed, one option is to climb into a half loop and then roll to wings level at the top. You traded airspeed for the potential energy of altitude, and slowed to your "corner speed" in the process, chaging directions quickly. At the end of the maneuver, you preserved energy and have some "in the bank" in the form of altitude. But once you are out of altitude, the fun has to go down a peg if you don't have the power in the first place. :D

[vintage1]

Mike:

What makes you think that the F16 is not doung 9G corners with a partially or fully stalled wing?

At best, the thrust of a jet fighter is about equal to the plane weight, or a bit more on empty tanks with full reheat..so it cannot be that which allows it to do a 9g turn when the wing theoretically is stalled.

I think the truth of the matter is, that whilst its easy to calculate where transition from (mostly) laminar to (mostly) turbulent airflow happens - the stall speed - what happens thereafter is a strange and difficult process to model, let alone calculate.

If the stall is characterised by a rapid rise in drag, and possibly even a small drop in lift at a given angle of attack, there is nothing to say that upping the angle of attack will not continue to increase the lift, albeit at a huge drag penalty.

I suspect that is what is happening: The thrust is used to not generate cornering force, but to overcome the huge drag of a partially stalled wing, which then does the cornering.

You can see this at airshows - the planes appear to be drifting outwards with respect to the direction the plane is pointing, and there is a huge amount of turbulence coming off them, with often condensation over the upper surfaces where the pressure is very low, and presumably massive pressure rises on the undersurfaces. That isn't laminar flow, and, indeed the airspeeds are probably high enough that compressibility effects make some of the simple airflow calcs invalid anyway - they must be getting near sonic speeds over parts of the wing.

How they arrive at the wing shapes lord alone knows :) Presumably lots of wind tunnel time. Given that they lower speed stuff can be optimised with flaps etc, the high speed wing wants to do three basic things - be very slippery at subsonic cruising speeds, achieve transonic and supersonic flight without too much drag or center of pressure changes - tho the latter can be tuned out with software - and generate huge amounts of lift at very high angles of attack, to give extreme manouverability in the subsonic region. But the latter does not have to be done in low drag modes.

I suppose what I am saying is that stalling is a way of saying that the wing suddenly generates rapidly rising drag as the AOA increases. Provided that the lift doesn't decrease as well, who cares as long as you have a big jet turbine to keep the speed up?

[Sparky Paul]

Mike notes the stall speed (calculated) for a 89.9 degree banked turn on a model is 300+ mph. All of us have flown models at 90 degrees of bank, and hardly achieve 300 mph to maintain altitude.
A little top rudder on my Kadet and it will climb in that condition... Vmax is probably 75 mph for that airplane.
So something more than what the simple equation states is going on. :D

[Eddie P]

Originally posted by vintage1
What makes you think that the F16 is not doung 9G corners with a partially or fully stalled wing?........
......If the stall is characterised by a rapid rise in drag, and possibly even a small drop in lift at a given angle of attack, there is nothing to say that upping the angle of attack will not continue to increase the lift, albeit at a huge drag penalty.

Partially stalled wing, yes, that's where a full performance turn is residing. Your observations are very intuative. Seeing a fighter in a hard bank and the track of the jet being different than where it's pointed with low pressure misting occuring over the tops of the wings shows the AOA of the wing and the wing itself working hard in this regime. It is still below a pre-determined hard critical AOA value found in wind tunnel and test flight data though.

Fully stalled wing, no. Another way of describing a stall in pilot terms is to call it a "departure from controlled flight." When a FULL stall occurs in a high speed jet of any type, it can take up to 10,000 feet or more of altitude loss to recover depending on the aircraft weight and configuration.

Upping the angle of attack once in a partial stall will get you right into a full stall. A full stall is charachterised by an exorbitant increase in drag and a DECREASE in lift. As drag increases, speed decreases, lift decreases further - it is a cascading event. Using thrust to continue in a fully stalled turn will only work with thrust vecoring, and then a turn isn't happening so much as a pivot while recovery efforts are made to get the wing flying again.

Sparky Paul- I agree, a 90 degree bank is harmless as long as you don't pull too hard for your energy state. Making up some of the lift lost by using the fuselage and vertical stab works great. Pyloners do this, as they ride slightly nose high or partially knife edged in hard left turns. :D

[Sparky Paul]

Ed, I was talking to a long-time ADP guy, Frank Harvey about his experiences with Lockheed since 1939, and he related a flight he had in an F-104D with Ed Brown as pilot in the early '50s .
He noted in a steep turn at Mach 2 it was easily observed that the plane was not flying a circle, but mushing out while maintaining a hefty g load.
.
Pylon racers easily get to 40g in the turn. Well beyond anything "computable" in terms of Cl/alpha.