Aspect ratio n taper ratio
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As for the first question, this is what I recall:
L=1/2*rho*TAS^2*CL*S
Firstly you represent the graph of "coefficient of lift" against "angle of attack" and let's assume that it's a symmetrical aerofoil. In this case the curve starts at the origin. Take the following as an example:
Aspect ratio = wingspan / mean chord.
Now if we increase the aspect ratio (which can be achieved by either increasing wingspan or decreasing mean chord) the gradient of the graph "coefficient of lift" against "angle of attack" is increased, i.e. it becomes steeper, however the maximum coefficient of lift stays constant. As this occurs the critical angle of attack is decreased (i.e. it may fall to 10 degrees or below).
From this you can deduce that if we were to maintain a given angle of attack, say 10 degrees and we'd increase the aspect ratio, assuming all other factors remain constant and the new critical angle is above 10 degrees, we would now have a higher coefficient of lift for that same angle of attack. Therefore referring back to the lift formula, as coefficient of lift increases the overall lift increases.
Bear in mind that: wing surface = mean chord * wingspan
Let's assume that we change both mean chord and wingspan in such a way that the wing surface remains constant, otherwise we would have to consider the change in wing surface in the lift formula too.
Let someone correct me on this if possible.
L=1/2*rho*TAS^2*CL*S
Firstly you represent the graph of "coefficient of lift" against "angle of attack" and let's assume that it's a symmetrical aerofoil. In this case the curve starts at the origin. Take the following as an example:
Aspect ratio = wingspan / mean chord.
Now if we increase the aspect ratio (which can be achieved by either increasing wingspan or decreasing mean chord) the gradient of the graph "coefficient of lift" against "angle of attack" is increased, i.e. it becomes steeper, however the maximum coefficient of lift stays constant. As this occurs the critical angle of attack is decreased (i.e. it may fall to 10 degrees or below).
From this you can deduce that if we were to maintain a given angle of attack, say 10 degrees and we'd increase the aspect ratio, assuming all other factors remain constant and the new critical angle is above 10 degrees, we would now have a higher coefficient of lift for that same angle of attack. Therefore referring back to the lift formula, as coefficient of lift increases the overall lift increases.
Bear in mind that: wing surface = mean chord * wingspan
Let's assume that we change both mean chord and wingspan in such a way that the wing surface remains constant, otherwise we would have to consider the change in wing surface in the lift formula too.
Let someone correct me on this if possible.
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and your 2nd question:
The main reason of tapering the wing is to reduce wing tip vortices and therefore reduce induced drag.
Your question is kinda backwards to expected, advantages of a low taper ratio (i.e more rectangular)
The optimum planform for reduced drag is an elliptical shape, and at the opposite end is a rectangular planform.
However, reasons for lower taper ratio include favourable stall characteristics (most important) and lower cost.
A compromise is found by tapering the wing.
The main reason of tapering the wing is to reduce wing tip vortices and therefore reduce induced drag.
Your question is kinda backwards to expected, advantages of a low taper ratio (i.e more rectangular)
The optimum planform for reduced drag is an elliptical shape, and at the opposite end is a rectangular planform.
However, reasons for lower taper ratio include favourable stall characteristics (most important) and lower cost.
A compromise is found by tapering the wing.
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Higher aspect ratio means lower induced drag. If I remember correctly the coefficient of induced drag = the coefficient of lift squared divided by pi times the aspect ratio.
Two problems with high aspect ratio are structure and Reynolds number. A high aspect ratio means a short chord and hence a shallow, hence heavy and/or expensive spar. The short chord will also reduce the Reynolds number.
An eliptical wing is ideal from the point of view of lift distribution but is difficult and expensive to produce.
A straight wing, no taper, is not good from the point of view of lift distribution but should give a fairly benign stall as the root will stall first.
A strongly tapered wing will delight the structural engineer but combine a fairly poor lift distribution with a nasty tip stall.
A moderatly tapered wing can give a good compromise. Even better is a double tapered wing which can get pretty close to the eliptical wing for lift distribution while being more practical to produce.
Two problems with high aspect ratio are structure and Reynolds number. A high aspect ratio means a short chord and hence a shallow, hence heavy and/or expensive spar. The short chord will also reduce the Reynolds number.
An eliptical wing is ideal from the point of view of lift distribution but is difficult and expensive to produce.
A straight wing, no taper, is not good from the point of view of lift distribution but should give a fairly benign stall as the root will stall first.
A strongly tapered wing will delight the structural engineer but combine a fairly poor lift distribution with a nasty tip stall.
A moderatly tapered wing can give a good compromise. Even better is a double tapered wing which can get pretty close to the eliptical wing for lift distribution while being more practical to produce.
