Weight shift
You are about to change one thing — move a battery, fit trim ballast, take the tail dolly off. How far does the centre of gravity go? There are two formulas for this, they look almost identical, and the difference between them is the reason people get it wrong exactly when the weight is big enough to matter.
The unit buttons only change the labels. Every number has to be in the same pair of units as the others, and which pair is up to you — the arithmetic does not care, but mixing them silently ruins the answer.
The centre of gravity moves
If your arms increase toward the tail, that is .
- New CG
- Total weight after
- Per unit of weight
Using the shift formula here — dividing by the old total — would have given , which is % out. The gap grows with the weight you are adding, which is why the mistake survives until it matters.
moving: ΔCG = w · d ÷ W
adding: ΔCG = w · (a − CG) ÷ (W + w)
- ΔCG
- how far the centre of gravity moves
- w
- the weight moved, added, or removed as a negative
- d
- how far it moved
- a
- the arm the weight arrives at
- CG
- where the aircraft balanced before
- W
- total weight before the change
The difference is the denominator. Moving something leaves the total alone; adding does not, so the second divides by W + w. The second reduces to the first as w becomes small against W, which is exactly why using the wrong one usually works and then suddenly does not.
Why the tail wins every argument
The moment a weight contributes is the weight times its distance from the datum, so a small mass a long way out does what a large mass close in does. In a glider the fin is metres from the centre of gravity and the cockpit is not, and that ratio is brutal.
Try it: put three kilograms in the tail at a long arm, then work out how much you would have to change in the cockpit to match it. The cockpit figure is usually several times larger, and on some airframes it is larger than any pilot you could legally carry. This is why tail tanks and fin ballast exist, why they are placarded so carefully, and why a forgotten tail dolly is a real incident rather than a joke.
It cuts the other way too. Water in the wings sits close to the centre of gravity, so it changes your mass and your wing loading a great deal and your balance hardly at all — which is why ballast is a performance decision rather than a balance one. Whether it pays is a different question with a different page.
Where this sits
This page answers “I am about to change one thing — how far does it move the CG?” and needs one number from your paperwork to do it. If you want the CG itself, worked out from every station with the envelope checked against it, the weight and balance calculator is the page for that, and it will also tell you the pilot-weight window your aircraft allows and which limit is binding it.
What this assumes, and what it can't know
Arithmetic on your numbers, and nothing else. No arms, no limits, no ballast positions for any type. The datum, the arms and the current CG all come from the weighing report and flight manual for the airframe in front of you.
The sign depends on your datum convention. This page assumes arms increase toward the tail, which is usual and not universal. If yours runs the other way the magnitude is still right and “aft” and “forward” are swapped.
A movement is not a verdict. Knowing the CG moved 40 mm aft tells you nothing about whether it is still inside the envelope. That needs the limits, and it is the other page.
Ballast has to be approved and secured. Trim weights are placarded per aircraft, in approved positions, properly fixed. Arithmetic showing that some mass would fix your balance is not authority to put it there.
Not yet checked by anyone but me. If you instruct, or one of these assumptions is wrong, I would genuinely rather hear it than not — tell me and I will credit you here. This is ground school, not a flight computer, and not an authority on your aircraft. Fly the numbers in your own flight manual and the instruments in front of you.