Answer:
Step-by-step explanation:
The minimum angle of glide, θ, can be calculated using the following formula:
θ = arctan(1/L)
where L is the lift-to-drag ratio.
The lift-to-drag ratio, L, is given by:
L = (CL/CD)
where CL is the lift coefficient.
For an elliptical wing, the lift coefficient is given by:
CL = (2πAR)/(2 + √(4 + (AR×e/0.9)^2))
where AR is the aspect ratio and e is the Oswald efficiency factor, which is assumed to be 0.9 for an elliptical wing.
For the given elliptical wing with an aspect ratio of 6, the lift coefficient is:
CL = (2π×6)/(2 + √(4 + (6×0.9/0.9)^2)) = 1.408
The drag coefficient is given by:
CD = 0.02 + 0.06G
where G is the lift-induced drag factor, given by:
G = (CL^2)/(π×AR×e)
For the elliptical wing with an aspect ratio of 6, G is:
G = (1.408^2)/(π×6×0.9) = 0.084
Therefore, the drag coefficient is:
CD = 0.02 + 0.06×0.084 = 0.025
The lift-to-drag ratio, L, is:
L = CL/CD = 1.408/0.025 = 56.32
The minimum angle of glide, θ, for the elliptical wing with an aspect ratio of 6 is:
θ = arctan(1/L) = arctan(1/56.32) = 1.06°
For the same elliptical wing with an aspect ratio of 10, the lift coefficient is:
CL = (2π×10)/(2 + √(4 + (10×0.9/0.9)^2)) = 1.496
The lift-induced drag factor, G, is:
G = (1.496^2)/(π×10×0.9) = 0.120
The drag coefficient is:
CD = 0.02 + 0.06×0.120 = 0.0272
The lift-to-drag ratio, L, is:
L = CL/CD = 1.496/0.0272 = 55.00
The minimum angle of glide, θ, for the elliptical wing with an aspect ratio of 10 is:
θ = arctan(1/L) = arctan(1/55.00) = 1.04°
Therefore, the change in minimum angle of glide if the aspect ratio is increased from 6 to 10 is:
Δθ = 1.06° - 1.04° = 0.02°
The change in minimum angle of glide is very small, indicating that the effect of changing the aspect ratio from 6 to 10 is not significant for the given wing geometry and drag coefficient.