Hi Sundance, thanks, just what I needed to stir my brain of a morning

So assuming that you are keeping everything else constant - speed, weight, span and air density - then there will be no change in actual induced drag. By doubling the chord you are doubling area and halving aspect ratio.

If you look at the equation for Induced Drag (Di) and not Induced Drag Coefficient (CDi) you will see that there is no representation for area or aspect ratio and so changing these has no effect.

In the above we can assume that lift (L) is the same as Weight. Air Density (ρ or rho), Speed (V) and span (b) are unchanged so the resulting actual induced drag (Di) remains the same.

The Induced Drag Coefficient (CDi)

**will** change however because area (S) is there in the formula:

Looking at the first version there - S is doubled, so for Di to remain constant, CDi must be halved.

Looking at the second version ie rearranged to show aspect ratio - it's easy to get hung up on the 'effect' of aspect ratio. But don't forget that the CL also changes too

because S is involved in the formula:

In fact CL and CDi are both halved and so actual drag Di still remains the same.

To think of it practically, induced drag can be visualised as the effect of tilting the wing back as you increase angle of attack. The greater the angle of attack (and CL), the more the lift vector is tilted rearwards. This rearward component of the lift is the induced drag, a force acting against the direction of travel.

If you double the wing chord but keep everything else including speed constant, the wing will be flying at a lower angle of attack ie half the CL. The CDi is also halved. But the actual total induced drag remains the same.

The

*overall* drag may well change a little. Profile drag may be reduced due to doubling the Reynolds number, but wetted area will have increased. The aircraft will also be in a different attitude which may affect parasite drag if the fuselage alignment has changed.

All of this is a little counterintuitive because it's easy to get hung up on the CDi formula and misunderstand the effect of aspect ratio. In reality all that matters for total Induced drag is

**span** - the more the better! Where span and weight is fixed then aspect ratio doesn't change as much as you might think.

(All of this assumes you want to keep speed as a constant. If you want to keep CL constant then the speed would change and the total drag would also.)

Jon

Induced Drag

Induced Drag

Induced Drag