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G tolerances for designs

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Old 02-03-2004, 06:15 PM
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Mike James
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Default G tolerances for designs

Howdy...

I used to have a book that had some examples for various airspeeds, showing typical G-forces imposed on airframes. I can't find the book now. So, the numbers below are rough guesses from my rusty memory.

I would guess that maximum G forces, including a 15% safety margin, for typical .60-size planes are approximately:

• Trainers or Scale 7 Gs
• Sport/Pattern/Jets 15 Gs
• Dynamic Soaring 40 Gs (!)
• Pylon Racers 30 Gs

Does anyone have more accurate numbers, or a formula that can give us better guidlines? Knowing these numbers would help any designer, enabling destructive testing, and also avoiding over-building components.

To all math geniuses who contribute, thanks.
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Old 02-04-2004, 05:17 AM
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Red B.
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Default RE: G tolerances for designs

Hi Mike!

The maximum number of G that an aircraft is subjected to (in the looping plane) depends on the speed, wing loading and maximum lift coefficient of the airfoil.

The formula simply is

G = 0.5 * rho * v^2 * S * Cl / m / g

where
rho = air density = 1.2 kg/m^3
v = air speed in meters/second (= speed in mph. * 0.447)
S = wing area in square meters (= sq.in. * 0.000645)
Cl = maximum lift coefficient (aprroximately equal to 1 for most aerobatic aircraft airfoils)
m = mass of aircraft in kg (= lbs. * 0.454)
g = earth gravity = 9.81 (Newtons/kg)


Example: A typical .40-sized aircraft flying at 70 mph. entering a loop using as much elevator as possible:

v = 70 mph. = 31.3 m/s
Wing area = 550 sq.in. = 0.355 m^2
Cl = 1
m =5.5 lbs = 2.50 kg

==> G = 0,5 * 1,2 * 31.3^2 * 0.355 * 1 / 2.5 / 9.81 = 8.5

i.e. the aircraft is subjected to 8.5 G.

In level turns the number of G is easily computed as:

G = 1 / cos(bank angle)

Example:
Bank angle = 45 deg ==> G = 1 / cos(45) = 1 / 0.707 = 1.4
Bank angle = 60 deg ==> G = 1 / cos(60) = 1 / 0.5 = 2
Bank angle = 90 deg ==> G = infinite, i.e. it is not possible to sustain a 90 deg banked level turn unless some amount of lift is obtained from the fuseleage of the aircraft, i.e. knife edge flight.



/Red B.
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Old 02-04-2004, 11:15 AM
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Mike James
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Default RE: G tolerances for designs

Thank you for the precision answer! It's exactly what I was looking for.
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