Islander stated it pretty well but seems to come to the same conclusion as me. (wrongly by the looks so far) In fact we were looking through the Hurt text at the aeroclub yesterday trying to figure this out in which those very formula seem to prove us wrong.
Originally Posted by
Islander2
i) Aerodynamics for Naval Aviators by H.H.Hurt, which is the aerodynamics text for US Navy aviators, and which takes seven pages to explain the complexities of maximum performance tactical turning, in the process considering lift limits, strength limits and power limits.
Turn radius is a function of Vē/tanAoB and turn rate is a function of tanAoB/V. It is mathematically impossible for V=minimum radius to be the same as V=max rate!
ASRAAMTOO, you raise a very good point though! Radius lines on a Rate over Speed chart are
straight... So there must be a squared relationship lurking somewhere that cancels out the Vē in the radius formula? Thinking about it.. well of course there is.. it is the fact that we are using stall speed for each load factor (equivalent to AoB) as the very V and assuming that stall speed increases
√G There you go!
Back to the Theoretical Aerobatic a/c Vs 60kt, 8G, Va=170kt Sea Level:
- Min Radius Turn:
R322ft, 51°/s @ 170kt AoB 82.9° 8G
- Max Rate Turn:
R322ft, 51°/s @ 170kt AoB 82.9° 8G
- 2.6G for Ref. to F16 Min Radius Turn:
R347ft, 27°/s @ 96kt AoB 67.1° 2.6G
Now if you have boat loads of power/thrust and a shallow drop on the back side of the C/L curve maybe you can reduce your radius by fudging your V flying back of the bucket. But something tells me that if you are going to pick your spot on the C/L curve for radius that rate would also tighten up to match it so long as you can still maintain your load factor... Ps=0
Here is the Mustang for an aircraft devoid of trickery and a definable stall break. Green is combat flaps and Blue is clean. Notice how the radius lines still intersect at higher rates/velocity/load factors.
So is that the answer then? Max rate velocity = Min radius velocity at a given load factor or position on the C/L curve? Anyone disagree?
P51