Wednesday, September 5th, 2012 09:54 am GMT -7 Wednesday, September 5th, 2012 09:54 am GMT -7Wednesday, September 5th, 2012 09:54 am GMT -7
USAF B-2 Spirit Stealth Tailless Flying Wing Bomber

Where should you put the center of gravity (CG) on a flying wing?




Shifted Center of Lift

Wing sweep pushes the air towards the wing tips. This is because the swept leading edge pushes the air sideways. The effect gets stronger and stronger the closer you move towards the wing tip. When you reach the wing tip, the air could be moving right along the wing span, instead of straight back. This is called cross span flow.

Note that I am talking about swept back wings. Swept forward wings experience a similar effect but in reverse. Since they are far less common, I will not say anything else about them.

There are a couple of consequences of this cross span flow. First, there is lower air speed flowing across the root of the wing. Lower speed means less lift. Second, the cross span flow effectively increases the Reynolds number at the wing tips. A side-effect is that the wing tips are now better at producing lift than they would have been otherwise.

With less lift in the wing center section and more lift at the swept wing tips, the net effect is that the center of lift is shifted rearwards.

Middle Effect

Early flying wing researchers about fifty years ago were very puzzled by this. The Horten Brothers called it the middle effect and thought it was caused by turbulence at the wing root. Their solution to the problem was to increase the chord at the wing root and to decrease the chord at the wing tips. That gave a more even lift distribution.

Affects Conventional Airplanes

This cross span flow affects conventional airplanes just as much as it affects flying wings. But conventional airplane wings are usually not very swept, so the effect is not very strong.

Also, the fuselage in a conventional airplane masks the loss of lift in the center.

CG Calculations

The standard method for computing the correct location for the center of gravity (CG) uses the mean aerodynamic chord (MAC), neutral point, and the static pitch stability margin. Problem is, this algorithm does not take into account the cross span flow.

What ends up happening is that the center of lift is further back than you expect, and therefore the stability margin is larger than you intended. Bottom line? The flying wing comes out nose heavy.

Computing the correct center of lift for a swept flying wing is trivial to do with a computer. It is harder to do with paper and pencil. In fact, computing the exact location using paper and pencil is very hard to do.

Proposed Solution

I would compute the location of the CG using the traditional method and fly the model like that, knowing that is is very likely nose heavy. Make sure you have plenty of elevator authority to still flare during the landing.

Once you have the rest of the model sorted out, start moving the CG back. Every time you move it, go through the standard set of tests to see if the CG is in the right location. Go easy and only move it back a little bit at a time. Sooner or later you are going to get the flying qualities you are looking for.

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