Turn Rate Formula

[clerick]

When i was unpacking some books i ran across an old one that came with Falcon Gold WAY back in the 90's.  It's called "Art of the Kill", interesting book but in it the author mentions a formula for turn rate

TR = K G/V

G = the g's the aircraft is pulling in the turn
V = is velocity

but K is only listed as a constant.  I would assume that this constant varies from plane to plane.  Could any of you explain what K represents and how it is derived?

[SkyRock]

Originally posted by clerick
When i was unpacking some books i ran across an old one that came with Falcon Gold WAY back in the 90's.  It's called "Art of the Kill", interesting book but in it the author mentions a formula for turn rate

TR = K G/V

G = the g's the aircraft is pulling in the turn
V = is velocity

but K is only listed as a constant.  I would assume that this constant varies from plane to plane.  Could any of you explain what K represents and how it is derived?

*see widewing!:aok

[clerick]

LOL.... now that you mention it i was kind of hoping he would drop by and enlighten me.  

[Angry Samoan]

Mosq !

[clerick]

Originally posted by Angry Samoan
Mosq !

riiiiiiiiiight.....  move along now, GIT!

[Stoney74]

Originally posted by clerick
When i was unpacking some books i ran across an old one that came with Falcon Gold WAY back in the 90's.  It's called "Art of the Kill", interesting book but in it the author mentions a formula for turn rate

TR = K G/V

G = the g's the aircraft is pulling in the turn
V = is velocity

but K is only listed as a constant.  I would assume that this constant varies from plane to plane.  Could any of you explain what K represents and how it is derived?

Could be "Drag due to lift"--aka induced drag.  A formula for K is

K = 1 / pi*e*A, where pi equals 3.14, e is Oswald's Span Efficiency Factor, and A is aspect ratio.  Might want to simply substitute a value between .75 and .85 for e.  Aspect ratio should be the wingspan^2 / wing area in ft^2...

[dtango]

TR = K * g / V

Hmmm... that's a funny equation.  Are you sure you have transposed it here correctly?

The only turn rate equation that is remotely similar that I'm aware of is:

TR = tan(b) * g / V

This is as close to your's as I can get by replacing K with tan(b).  In this equation g isn't g-load but gravitational acceleration (a constant).  (b) is bank angle.

tan(b) is usually substituted as a function of load-factor n (g-load of the aircraft).  This form of the turn rate equation is:



Tango, XO
412th FS Braunco Mustangs

[MORAY37]

Originally posted by dtango
TR = K * g / V

Hmmm... that's a funny equation.  Are you sure you have transposed it here correctly?

The only turn rate equation that is remotely similar that I'm aware of is:

TR = tan(b) * g / V

This is as close to your's as I can get by replacing K with tan(b).  In this equation g isn't g-load but gravitational acceleration (a constant).  (b) is bank angle.

tan(b) is usually substituted as a function of load-factor n (g-load of the aircraft).  This form of the turn rate equation is:



Tango, XO
412th FS Braunco Mustangs

That is the formula I'm aware of as well.

[68Hawk]

So like, 1+1 is still 3 right?

[Gianlupo]

Clerick, give a look at Brooke's page about Math behind turning:

http://www.electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/turningMath.html

I think you'll find there all you want to know.

[Roughshod]

The maths behind displacing inertia into a different direction with least loss is...Look at how a noob tries to do it, then relate how you know how to do it, and call it intuitive experience that defines mathematics...(when you getting shot at often makes  mathematical principles quite clear aand most times rather accidentally...though one has to reliaze that Aces High is a computor model trying to relate to the real thing)

So maybe its best to experiment with the Aces High model of all these forces and maybe realize, it quite likely does not represent the 'real deal'

[BaldEagl]

Who cares?  In the middle of a fight it doesn't matter if I've got a mathematical chance of winning or not,  I'm still going to die.

[Gianlupo]

It doesn't seem to me that clerick asked anything about AH flight model or said he wanted to calculate his turn rate in the middle of a fight. He just plainly asked for a real life formula.

[porkfrog]

In light of my scientific analysis of the above conversation, I have come to one obvious conclusion.


1. I am a COMPLETE idiot in regards to math.


Although there are some who would say I'm just a complete idiot.

[clerick]

I'm an engineering student and as such i tend to be drawn to formulas.  I asked the question merely out of curiosity.  

I did double check the formula and I presented it exactly as written in the book.  What i don't know for sure is if "G" is indicated g's in the turn or radial g.  I would assume that it is radial g.

Looking at Gianlupo's website i think I've found my "K".

omega = (g / v) * sqrt[(L/W)^2 - 1]

it would appear that sqrt[(L/W)^2 - 1] = K.  Though the author uses g instead of G.  I can's see where he defines g. Classical physics would say that it is the force due to gravity, but looking at the formula the website offers i will assume that it is sloppy math since his formula appears to disregard the g's the aircraft is pulling.