Conference vmszoo::rc

43.0. "Scaling Magazine Plans" by CLOSUS::TAVARES (John--Stay low, keep moving) Fri Feb 06 1987 16:28

I've been doing a little button pushing in scaling plans from RCM,
and I thought I'd write a note to record my method.

The model is a trainer called Bambi, from the mid to late '70s (the
date on the issue is missing) it is a very simple model, the
relevant thing is that the wing is a nearly perfect rectangle.  The
original model is meant for a .19 to .30 size engine.  I would like
to build the model at full size as a back-up to my Eaglet.  In
looking at the plans, I also thought it would be a nice model to
build as an electric for my Astro .035.  Thus the button pushing.

1.  Determine the scale factor between the old wing area, and the
new wing area.  This is not quite as simple as it sounds; RCM plays
a little trick on the unwary.  As you know, they give dimensions
along with their articles.  For Bambi, the wing area, A, was given
as 504 sq in.  Wing span, S, was given at 56 inches, wing chord, C,
was given at 9 inches.  They must take these dimensions off the
completed model, because in the years I've been measuring RCM plans
against dimensions, they are seldom correct.  

With these plans, the wing on the page was 9 5/8 inches long; using
the scale on the drawing of 6"=1", I found that the plan view of the
wingspan was 57.75 inches.  The chord measured true at 1.5"; giving
a chord of 9" as they published.  Multiplying C X S; 57.75 x 9; I
found that the actual plan wing area was 519.75 inches.  These are the
numbers to use in scaling.

We will find the same thing when we go for the fuselage dimensions;
the given fuse length was 37 inches, but from the plan it was more
like 39 inches; the difference was due to the curvature of the sides
when measured off the finished plane. 

2.Now use the formula
     ______________
    / new wing area
   /  ------------- 
  /   old wing area

This is supposed to be the "square root of the term new wing area,
divided by the old wing area; or, the square root of 250, my new
wing area, divided by the plan wing area, 519.75.  For accuracy, you
must take the numbers out as far as your calculator will go.  The
scale factor should be stored in memory to preserve the accuracy of
the result.  In this case, I found that my new wing area was .6935
the size of the old wing area.  

3.Find the span and chord of this wing:

Old wing span x scale factor = new wing span; 57.75 x .6935 = 40.05 
Old wing chord x S.F. = new wing chord; 9 x .6935 = 6.241
New wing area; 6.241 x 40.05 = 249.974 sq in. (this is a check)

I have to perform these steps to get the correct ratio of span and
chord for my new wing.

4. So, if I multiply all the dimensions of the full size model by
.6935 (remember that the rest of this number is hidden in the
calculator; in my HP it is a 10 place number) we will have the
dimensions for the new model.  But why go through the extra step of
taking the dimensions off the plan, scaling them up to full size,
then reducing them down to the new size?

5.Now I go back to the plan and take the 9 5/8 that they give me,
and find how big I have to scale it up to get the 40.05 inch span;

 40.05
------- = 4.161
 9.625

So, if I multiply all the plan dimensions by 4.161 (again, keeping
this number in memory for accuracy), I will scale up the model to my
required dimensions:

 9.625 x 4.161 = 40.05 (I'm pedantic)
 1.5 x 4.161 = 6.241 (this is the chord on the plan times the scale
 factor)
....and so on throughout the plan.

As a check on my math, I take the dimensions from the last
calculation and multiply; 40.05 x 6.241 = 249.974 to get the area of
my new wing.  Close enough for government work!

    My uncle once told me, "It's okay to scale UP, but NEVER scale DOWN!"
    
    When I was in high school I needed a good three channel plane for
    my Enya .09. After reviewing my library of RCM back-issues, I 
    chose an attractive .60 design, with the intention of scaling down.
    
    Since I was planning to use the "plans" printed in the magazine,
    scaling was a piece of cake---instead of multiplying the page-measured
    value by a factor appropriate for the full-sized plane, I multiplied
    by a factor which would yield the wingspan, etc, which I desired.
    I believe the resultant wingspan was between 36 and 40 inches.
    
    So I built the plane, and noticed the first problem---while the
    dimensions may scale nicely, the weight doesn't! And neither does
    the bulk of the radio! Anyway, I positioned the equipment as best
    I could, to obtain the best CG.
    
    My uncle (who, at that time, had over ten years of RC experience)
    had the honors of the first test flight. I hand launched the bird,
    and it lept into the air with the Enya whining away. It rocked
    along its longitudinal axis a bit, and my uncle commented about
    its unstable nature and its need for ailerons. He spoke between
    breaths, as he was working his buns off keeping it staight and
    climbing---we're still talking about take-off here!
    
    When it was to a "safe" altitude, he announced that he would try
    a left turn. It would be rudder-and-elevator, which bothered him
    since it had been a while. But his experience includes rubber-band
    escapements, so he was a minor diety.
    
    He started the bank. It looked nice, but it suddenly flipped on
    its back. He found himself flying up-side down! So he tried to 
    use the rudder and elevator to right the plane, but it would only
    roll. In the many attempts we were chewing up the sky and losing
    precious altitude.
    
    Finally a bad elevator-rudder combination stalled her, and she 
    went into a spin. Uncle Jim damn near recovered; he stopped the
    spin and was pulling out inverted (how he kept "up" and "down"
    straight, I'll never know) when he simply ran out of sky. 
    
    Not much damage, since there wasn't much plane to damage, but a
    ruptured fuel system messed up the fuselage. Red Max and cow manure
    all over the place! 
    
    The lessons: (a) Weight doesn't scale. To maintain nice performance,
                     consider making the wing and control surfaces larger
                     than your scaling factor would dictate.            
    
                 (b) As scale decreases by 'x', area decreases by 'x^2'.
                     See (a), above!
    
    My uncle actually enjoyed the challenge of test flying my creations;
    this was the second of three hair-brained experiments that he tested
    for me. One of them, a zero-dihedral wing with "barn-door" ailerons
    for a Kadet (pre-Mark II), preformed like a dream. But my uncle--that
    guy can FLY!