Mark1234

Anyone know how to work out the speed / config for a minimum radius of turn - so called corner speed I believe, more commonly used for fighting aeroplanes? I'm thinking wrt mountain flying.. for example if you happened to be up a blind alley!

BOAC

Good starting point is http://selair.selkirk.bc.ca/aerodyna...ft/Page13.html

Mark 1

It's a matter of maximising the "lift to velocity" ratio in a balanced turn. About half flap, full power and pull to the buffet will get you close.

Ballistic or semi-ballistic maneuvers can reduce it further e.g. stall turn (hammerhead) or a wing-over, but these need some vertical space to complete.

F4F

...

and SPEED


live 2 fly 2 live

Intruder

I suggest you read up on your basic flying principles and specific mountain flying texts, and forget the fighter pilot stuff for a while. Minimum turn radius is had with minimum speed and maximum bank/G.

"Cornering speed" has more to do with turn RATE than radius, and also has an aspect of sustainability in it.

18-Wheeler

Corner speed in a fighter is the speed at which ->
- not too slow as to run out of wing before running into the G-limit of the ariframe.
- Not too fast as to over-G the airframe with full deflection on the controls.
AFAIK it varies with altitude and configuration.
In an SU-27 it's about 750km/h.

Mark1234

@BOAC - Thanks, that was what I was looking for

@Mark1 - I wonder - theoretically I can load a 172 to considerably more clean than I can with flaps....

@Intruder - you are correct, I'd not considered the sustainability factor of corner speed. Anyway, forget calling it corner speed - It's min radius I'm interested in!

As for min speed, max bank - no:
At Vs, I cannot roll out of wings level/1g or I'll stall - I'm confined to a straight line, so it's not that.

At Vne/Vno (and anywhere above Va) I'll be limited by airframe load factors, and could pull just as hard at lower speed, which, with less Kinetic would turn tighter. Between those boundary conditions, there's going to be an optimum trade off of speed vs increased lift available from the wing.

In any case, fear not, I'm quite au-fait with basic aerodynamics, and I'm not about to plod into the mountains based on pprune advice, or even just reading books. Simply an idle tuesday afternoon wondering - I have V speeds for about everything else and set me thinking.

Mark 1

Mark1234 - If we solve your problem for a balanced level turn, with altitude and velocity stabilised throughout. The max angle of bank will be limited by the power available to maintain speed. To a first order that will be independent of configuration (actually depends on Cl/Cd at Cl-max).
For an example, let's say that this is at a load factor of 2 and hence for a 60 degree angle of bank.

In a stabilised turn at that angle of bank Cl-max will be reached at 1.4*Vs.

Let's assume that flaps increase Cl-max by 20% and so decrease stall speed by 10%.

The radius of turn is dictated by the centripetal component of lift and is proportional to (Velocity^2/tan(bank angle)).

As we have fixed bank angle for the two cases the radius of turn will be proportional to the square of the velocity at which you reach Cl-max.
So lowering flaps and increasing lift means that you reduce the velocity by 10% and hence reduce the radius by 20%.

The assumptions that I've used are far from perfect, but, I hope, explains the basic reasoning for using flaps and buffet speed (buffet is close to AoA for Cl-max) to minimise the turn radius.

Hope this helps.

M1

Intruder

You have to find the minimum speed at which you can sustain the max angle of bank for the duration you need (e.g., 180 degrees for your mountain scenario).

For example (and these are artificial numbers, so you'll have to research your own for your airplane), the minimum level speed in a C172 -- without going behind the power curve -- may be available at 20 deg flaps. At full power, you may be able to maintain 60 deg angle of bank (2 Gs) for 180 degrees at 60 knots. Your min radius will be attained in that configuration.

Since such performance numbers may not be readily available for most GA airplanes, you'll have to interpolate and analyze available data, then test in flight at a safe altitude.

MidgetBoy

Really? When I'm in a 172, if I were in a dead end in a valley, I'd:
1. Power idle.
2. Nose up to slow down, white arc, full flaps.
3. 90 degree bank.
4. Full power.
5. Recover after about 150 degree turn before I stall.
6. Keep a 45 degree bank still.
7. Power to cruise, bring up the flaps.
Done =P

Pugilistic Animus

min radius turn occurs at Va [Vp] It gives both the minimum speed required developing the aerodynamic load factors required for min radius turns and the maximum within the limits of strength

less than Va the limit load factors aren't available.... and the min radius can't be developed----aerodynamic limits


greater than Va, then CLmax and the and maximum load factors aren't available...structural limits


fooling with flaps is not too good because even though stall speeds are less, so are limit loads....watch it!

and tight turns in tight valleys with precipitous terrain--- unless your name is Patty Wagstaff or Mike Goulian


I could go on forever with math to prove this, but -----nah!

Mark1234

Midget boy - you may well find the wings fall off.. Not knowing where the structure really will fail, and using the placarded limits: the limits are 2G flaps out, 3.8 clean, so taking a level turn flaps limit you to 60deg bank. I don't know exactly what point the wings would really fall off, but...

Pugilistic animalus I'm convinced! the maths are in the first link BOAC posted.

And no, I'm not going to go and try it Thanks for all the info.

Intruder

While you may be correct for some airplanes in the instantaneous case, I don't think you would prevail for the sustained (180 deg turn) case. A few questions:
1) What civil aircraft can sustain Va at max allowable G and constant altitude? [I believe the answer is "None."]
2) What is the airspeed bleed rate, when starting at Va in a max G turn, for the airplane under discussion? [Yes, rhetorical, because it depends on the specific case.]
3) At what rate does the pilot have to relax G so he doesn't stall when the airspeed bleeds off? [Again, rhetorical for the same reason.]
4) If the alternative is colliding with a mountain, are you willing to overstress the airplane to minimize your turn radius? If the answer is "Yes," you may find that a 2.5 G turn (instead of the 2.0 G clean limit), 10 knots slower than clean speed, with 20 deg flaps, may give you the turn radius margin needed to miss that mountain.
5) If you start the turn with "excess" airspeed, using the vertical plane in a wingover maneuver will significantly reduce the turn radius. Again, power and altitude available may limit vertical maneuverability.

OK... What part of "r = V**2 / (g * tan(b)" (from that page) don't you understand?

The square of the velocity is the most significant term! Let's assume Va is 100 mph, a clean turn can be made at 70 mph, and a flaps-down turn can be made at 60 mph.

At Va and 3.8g (74 deg bank; cited by someone to be the limit), turn radius is 1521 per the formula (units are unknown and irrelevant; I'm speaking only relatively).

At 70 mph and 2.5 G, the radius is 856!

At 60 mph and 2 G, the radius is 1040; Reduce it to 628 if you can sustain 2.5 G!

So, either a clean turn at 66.5 deg bank or a flaps-down turn at 60 deg angle of bank will yield a smaller turn radius than the turn at Va and max G -- even disregarding sustainability!

Granted, reducing G by putting the flaps down will increase the turn radius. However, if you can sustain the same G as at a minimum speed clean turn, you come out ahead, with little risk of pulling off the wings (acknowledging the 150% design factor).

OzExpat

Where the hell are you planning to use this information? If you're going to experiment with this rubbish in a mountainous area then I don't expect to hear any more about this. Instead of learning the bl**dy THEORY, why the h*ll don't you take your chosen aeroplane type up to about 8,000 feet over a sea level environment and CAUTIOUSLY (note the emphasis) test things for yourself!

The reality is that, if you get into that situation in a mountainous area, you are MOST UNLIKELY (note the emphasis) to survive. If you are a professional pilot who's considering work for a company that operates in that sort of environment, let them TRAIN you for it. If you are not a professional pilot, either you're an accident statistic that's about to yet again smudge the name of GA all over the countryside, or you will leave such an environment to the professionals.

Mark1234

OzExpat - Oh for heaven's sake indeed DO pay attention and read the whole thread, before jumping in with both feet.. you might fall off that high horse if you're not careful.

For the record, I already stated it was a boring afternoon staring out the window at work and pondering. No practical usage intended; I'm rather too attached to this life to go testing out such barstool talk. Which is all it is - something that (to me anyway) is more interesting than the interminable discussion of football scores in the office.

Intruder.. I have to admit my brain's struggling with the maths, (and I got busy..) will think about it another day, but thanks.

Pugilistic Animus

Mark1234: there are 3 possible limiting factors which may limit or define max theoretical turning performance, they are:

1. The airfoil's ability to produce maximum lift---

Assuming a steady state process where L=W, since the maximum weight ever to be carried by a wing is the weight that it carries at the stall Vs.

Lmax = Clmax *QS=1/2rhoVsqrd*S--- And ---

W[at stall] =Clmax 1/2rhoVssqrd*S ---therefore---

g max or n [g=n] max = Lmax/Wmax...divide eq. 1, by 2 and all cancels except the 'V' terms, therefore nmax= [V/Vs]sqrd...so you now have now the max load factor possible: a stall at 2 vs will pull 4m*g or 4 W or 4 'g'---

a stall at 4*Vs creates load factors of 16g etc, etc...



2. The operating strength limitations: this is the upper limit of the load factors that will not hurt the airframe: Va again

From above pt.1--- you can derive that Va = Vs*sqrt n


3. Thrust or power limits ---

This defines the ability to maintain altitude.


As far as stall speed in a turn remember that n = L/W =1/Cos phi; phi = b= stall speed increase with bank angle is derived by recording that---
--- stall speed increases with W or g can be derived from Vs2/Vs1=sqrtW2/W1, so you may write that Vs[phi] =Vs*sqrt[n]

Lastly, as a hint to understand the web site---- remember that y =sin Theta, and X =cos theta, and sin /cos =Tan and Tan= opposite side length/ adjacent, or y/x


and for interest:

Rate of turn =1091Tan [phi] / V

and

increase in stall speed Vs with flaps is given, by

Vsf = sqrt*CLmax [clean] / Clmax [w/flaps]

BTW: turn radius at stall speed is infinite as you implied already--impossible!


math stuff on this site can be very cumbersome




Intruder: I was timed out at 2.00 am and couldn't repost I'll get back to you soon!

Pugilistic Animus

Intruder:

1, I believe an Extra 300S can! as it seems to meet all of the requirements listed above and is certified aerobatic under FAR part 23

2,3 very academic indeed---also as OzExpat implies...you've answed your own question

standby i have class---gotta do another long boring lecture

Intruder

Indeed, calculating "performance" is very tedious. However, in the context of the OP's original question, we are most interested in turn radius. Without knowing the specifics of the airplane involved (limit G, power available, etc), and knowing the OP is not an experimental test pilot with access to all the associated resources, simplifying assumptions serve well.

The link posted by BOAC gives enough information to get a handle on the problem. Using a few simplifying assumptions and/or example data (as I did above) serves to quantify the problem. Using numbers typical of light GA airplanes and disregarding vertical maneuvering, we now know that we can cut the turn radius by a factor of 2 by reducing airspeed from [the vicinity of] Va to Vy. Also, since excess power is maximized in the vicinity of Vy, that power can be put to good use in developing G.

OTOH, we also found that dropping flaps may not be a good idea in light GA airplanes, because the reduction in G available likely more than offsets the reduction in minimum maneuvering airspeed (which may be on the order of only 5-10 knots).

OTOOH, dropping flaps in a transport category airplane significantly reduces maneuvering speed (e.g., by 80+ knots in a 747) while only reducing limit G from 2.5 to 2.0, thereby becoming a distinct advantage in reducing turn radius.

wingnut_nz

MidgetBoy is on the right track. More info on the box canyon turn here:

www.mountainflying.com/pdf%20files/Box%20Canyon%20Turn.pdf

Slopey

Full flaps in an older 172 with the 40 degree setting in a 90 degree bank would be painful, but quick - no?

With the barn doors out the 172 I fly does'nt climb extraordinarily well even under full power, with a 90 degree bank angle on at idle, it would head for the deck sharpish.