[NSRCA-discussion] Balancing a Model

[Jay Marshall]

BALANCE THE EASY WEIGH

(c)J Marshall 2006

I have tried balancing large models both by using a "CG Machine" and the
pendulum technique with only a lot of trouble and moderate success. 
      
Having recently dropped a model during one of these exercises I wondered if
there wasn't an easier, and faster, way. By golly, I just remembered some of
the Statics course I took in engineering school some 40 years ago. Haven't
used it much since I am an EE, but good things hang around.  I had also
recently purchased a scale to use in building a Black Magic and wondered if
I couldn't use it in weighing and balancing a new model.

The technique I use has the added advantage of only requiring a small, 5
lbs. or less, scale, and also measures the total weight, lateral balance, CG
point, and enables calculations to move the GC by placing/moving  weight to
new positions.

Set up the model to be weighed by supporting the tail so that the fuselage
datum line is level. Be sure to support the tail and the wheel not being
weighed or the calculations will be off. Weigh each main wheel and the tail
wheel in the supported positions. The sum of these weights will be the total
weight of the model. 

Measure the distance on the centerline from the tail wheel axel to a point
perpendicular to the main wheel axel as L. The distance from the tail to the
CG will be Lt, and the distance from the CG to the main axel will be Lm,
therefore L = Lt + Lw.  By the same nomenclature, Wt is the tail weight and
Ww is the sum of the two main wheel weights. 

At the CG  Ww*Lw = Wt * Lt. We then substitute Lw = Wt*Lt/Ww into (1) and
solve for Lt. Use the answer to solve (1).  

For example we have the following:

L  =  47.75
Wt  =  364 g
Ww  =  2318 g
Lw = length from CG to main wheels
Lt = length from CG to tail wheel
Then: Lt =   364/2318L2 = 0.16 Lw

Substituting for Lw:
Lt* 0.16 + Lt= 47.5
1.16 Lt = 47.5
Lt = 41.2
And Lw = 6.55

Therefore the CG is 6.55 in. behind the wheels.

Now that we have a CG, how to we correct it? How much, for instance, do we
have to move the battery?

Assume we have a 125g battery located at 4 in. behind the CG that we can
move forward, and that we want to move the CG forward  0.4 in.

We can consider the original balance consisting of three vectors: L1 * Wn,
and L2 * Wt + Wb * Lb where Wb and Lb are the weight and moment of the
battery. The effective weight of the battery on the scale is Wb * Lb/Lt or
12.3g. Since we are going to move the battery we subtract this from the
measured tail weight for a new tail weight of 351.9g. The new nose weight
will now consist of the original and the new Wb*Lb. We know Wb so we must
adjust Lb so that Wt*Lt = Wb*Lb + Wn*Ln. 

This same method can be used to add a new weight to move the CG. The only
difference is that we don't subtract the weight from the tail and the new
W*L has two variables. We are free to choose one, such as the weight, and
the calculations will show us where to put it.

The scale can also be used to correct lateral balance without all of the
calculations. Just add wingtip weight until both LG match (assuming the
wheels are equal distance from the fuselage centerline).







Jay Marshall

-------------- next part --------------
A non-text attachment was scrubbed...
Name: winmail.dat
Type: application/ms-tnef
Size: 5220 bytes
Desc: not available
Url : http://lists.nsrca.org/pipermail/nsrca-discussion/attachments/20061018/93a4e9c8/attachment.bin