I think we need to clarify the relationship between airspeed and turn-radius. Here are some excerpts from something I posted awhile back.
Corner velocity is where an aircraft's maximum turn-rate, and minimum turn-radius occurs for a fixed aircraft configuration (e.g. no flaps etc.). Have a look at one of Badboy's past Energy-Maneuverability diagrams:
Here's an EM chart of the Spit MkI, Hurricane MkI, and Bf-109E. Notice the turn-radii for the aircraft. Turn-radius never gets smaller than the turn-radius at corner speed. Infact turn-radius actually increases the slower you get below corner speed. So what gives? Simply put, in a level turn below corner speed an airplane cannot generate as much lift as is possible at higher speeds up to corner, thus it can't turn as sharply. The reason is turn-radius is also a function of the maximum g-loading / turning-bank-angle that the aircraft can attain. Here is the level turn-radius equation:
Eventhough a lower airspeed reduces the numerator, the denominator also reduces with airspeed. Maximum turn load-factor "n" (g-load) and maximum turn bank-angle "theta" vary in direct proportion to airspeed. The lower the airspeed below corner, the lower the max g-load / bank angle an airplane can achieve.
Why is this? Because the slower we go below corner speed, the less lift we are able to achieve and thus the less we're able to turn.
In a level turn we need "vertical" lift to not only support the weight of the aircraft, but we also need additional lift in the "horizontal" direction to create angular acceleration to curve our flight path. Thus to turn we need to create more lift than weight of the airplane and incline the airplane at a bank angle to take advantage of the additional lift to turn the plane. The tighter the level turn, the more lift is needed in the horizontal direction as depicted below:
Remember that lift is directly proportional to lift coefficient (Cl) and airspeed squared. To increase lift we can either increase Cl by increasing angle-of-attack (elevator input), increase airspeed, or both. In a max performance turn, we can easily attain maximum lift coefficient by yanking back on the stick regardless of airspeed. If Cl is fixed at it's maximum through elevator input the only other variable that varies is airspeed. So if you're at Clmax and low airspeed, this is lower lift than obtainable compared to Clmax at a higher airspeed. Lower airspeed => lower lift => less capability to turn.
So how do we explain the charts from Dok Gonzo's website where turn radius is lower for lower airpseed? It all has to do with high-lift devices like flaps and slots. Remember that we can increase lift by increasing lift coefficient. High lift devices like flaps increase the maximum lift coefficient of an aircraft. This means this increases the amount of lift capable and also reduces the airspeed to create equivalent lift in a turn compared to the same aircraft without the high-lift device deployed. Here's another EM Chart from Badboy to demonstrate.
Notice the P-38 with no flaps vs. with 5 notches of flaps. The flaps enable the P-38 to decrease it's turn-radius from 800 ft (@260mph) down to below 600 ft (@195mph). This is because the flaps allow the aircraft to obtain a higher maximum lift coefficient. With flaps this enables the aircraft to obtain the equivalent lift with no flaps but at a much lower airspeed. Notice however that with 5 notches of flaps that the turn-radius increases (as we now expect) the lower below "corner speed" the airplane goes.
I hope that helps to enlighten the topic.
Tango, XO
412th FS Braunco Mustangs
