Mass & Balance - ATPL question

[MalteseJambo]

Probably this is an easy question but i cant get my head round it:

An aeroplane with a two wheel nose gear and four main wheels rests on the ground with a single nose wheel load of 500 kg and a single main wheel load of 6000 kg. The distance between the nose wheels and the main wheels is 10 meter. How far is the centre of gravity in front of the main wheels?

Without the distances aft of the datum how can i calculate the answer?

[Keith.Williams.]

The nose wheels are 10 m in front of the main wheels, so if the main wheels are taken as a datum, then the position of the main wheels is zero and that of the nose wheels is –10 m.

The total load and moments of each load can be calculated by adding up the loads on each wheel and using the standard equation:

Moment = load x arm.

Item...............................Load....Arm from main wheels...oment = load x arm
Nose wheel 1..................500 Kg.......-10 m....................-5000 Kg m
Nose wheel 2..................500 Kg.......-10 m....................-5000 Kg m
Left main wheel 1...........6000 Kg........Zero..................... Zero
Left main wheel 2...........6000 Kg........Zero..................... Zero
Right main wheel 1.........6000 Kg.........Zero..................... Zero
Right main wheel 2.........6000 Kg.........Zero.....................Zero

Totals.........................25000 Kg.................................-10000 Kg m


The C of G can now be calculated by using the standard equation:

C of G = Total moment /Total Mass

C of G = -10000 Kg m / 25000 kg = -0.4 m

This means that the C of G is 0.4 metre forward of the main wheels.

[Anders S]

Hey,

I've just stumbled upon this question, and could use an explanation myself. (In my text the single nose wheel load was 725 kg, but other than that identical.)

Cheers

[pudoc]

An aeroplane with a two wheel nose gear and four main wheels rests on the ground with a single nose wheel load of 500 kg and a single main wheel load of 6000 kg. The distance between the nose wheels and the main wheels is 10 meter. How far is the centre of gravity in front of the main wheels?


Ok so the best way is to draw it. For this question assume the nose wheels are on the datum. So you should have a diagram (a simple line will do) on the far left will be the nose wheels and on the far right the main wheels at 10m.

The formula for CG is momentum/mass, and momentum is calculated by mass x distance from the datum.

So:

Total mass at the nose wheel (at the datum): 1000kgs
Main wheel total mass: 24,000kgs

Let's apply the mom/mass formula...but wait, whats the total momentum?

To calculate the momentum the main wheel has (mass x arm) 24,000kgs x 10m = 240,000

Now, the nose wheel is located on the datum, so it's distance is 0. 1000 x 0 = 0.

Now we have the momentum and mass, let's calculate the CG.

CG = mom/mass

=240000/25000
=9.6m

So the CG is located 9.6m aft of the datum. And to answer the question, the CG must be 0.4m in front of the main wheels.

[Anders S]

Ah yes, that makes sence, cheers!