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# The Math (Gulp !)

In this post we take a look at some real world numbers for the Bearhawk. If this makes your eyes glaze over, feel free to skip right to the Conclusion.

The Bearhawk plans state that it is rated to:

4.5 G at 2500 lbs

5.0 G at 2300 lbs

This places it firmly in the Utility Category.

## Load Factor in a turn

Formula:

Load Factor = 1/COS Angle of Bank

Examples:

2.0 G = 1/COS 60° (Steep turn)

Bank Angles at which the aircraft would theoretically reach these limits:

4.5 G = 1/COS 77° at 2500lbs

5.0 G = 1/COS 78° at 2300lbs.

Therefore the bank angle at which the Bearhawk will reach it's rated load factor of 4.5G in level flight is 77° AOB.

## Stall Speed in a Turn

Stall-speed is proportional to the demand for lift.

As a turn steepens and the demand for lift increases, the stall speed increases.

Formula:

New Vs = Original Vs x √Load Factor

An example is a steep turn at 60° AOB. Using a load factor of 2.0 G (at 60°) and beginning with a (flaps up) stall speed at 2500lbs of 46 KTAS:

Vs at 60° = 46 x √2.0G = 65 KTAS

Vs at 77° = 46 x √4.5G = 97 KTAS

## Maneuvering Speed

This is the speed at which flight at the design load Limit will result in the wing stalling, thereby limiting it from reaching a higher load factor.

Formula:

Maneuvering Speed Va = Vs x √Load Factor

The maneuvering speed uses the formula above to find the stall speed that coincides with the maximum rated load factor. We have already established that in a level turn the Bearhawk will reach it's maximum rated load factor of 4.5 G at 77° AOB:

At 2500lbs Vs (Flaps up) = 46 KTAS

Va = 46 x √4.5G = 97 KTAS

At 2300lbs Vs (flaps up) is 42 KTAS.

Va = 42 x √5.0G = 94 KTAS

## Conclusions:

The following speeds are approximate as tested and calculated for one Bearhawk:

Vs (2500lbs) = 46 KTAS (Flaps up)

Vs (2300lbs) = 42 KTAS (Flaps up)

Va (2500lbs) = 97 KTAS

Va (2300lbs) = 94 KTAS

In a 60° banked turn the stall speed increases to 65 KTAS

In a 75° banked turn the stall speed increases to 90 KTAS

If flying at a speed below 94 KTAS the aircraft will stall before it reaches it's design load limit of 4.5 G. If flying at a speed above 94 KTAS then it is possible to exceed the design load limit.