cannonmn, Nice to hear from you. We sure did like your display at the Mansfield Artillery Show. You know, considering that Mike and I have more than 56 years of Aerospace and Aircraft Industry inspection and calibration experience, we were a little concerned about the effects of thermal expansion on the main, lengthwise member in the Sight Base assy. We did a few preliminary calculations and decided to go ahead with aluminum because it is so much easier and cleaner to work with than cast iron which we also considered. We outlined several experiments to perform on the prototype sight base which is almost identical to the one we use today. We always go to the high plains north of Denver, Colorado to do our accuracy testing where the temperature can rise 20 degrees in four hours. From May to September, our shooting season, we can expect it to be about 70 deg. F. when we start at 7 o'clock and about 90 deg. F. when we halt our cannon testing at 11 o'clock. On average, a 5 deg. F. rise can be expected per hour. We are deliberate, methodical and slow in our cannon shooting. We shoot one 5-shot group per hour, that's all.
Our experiments duplicated these conditions as much as possible in our climate controlled calibration lab where we calibrated precision Gage Blocks for industrial customers for eight years. The tolerance on these blocks is plus or minus .000002" ( 2 millionths of an inch). The sensitive Swiss and German electronic indicators we used are the same ones we used to calibrate these measurement standard, gage blocks. We made careful measurements of the length expansion and the up and down deflection of the main bar, the height expansion of the support pieces and the side to side deflection of the main bar during a five degree rise in ambient temp. over one hour. Remember that the expansion ratio of aluminum is 13 millionths of an inch per inch per 1 deg. F.
Maximum length expansion was .00018", (one ten-thousandth, 80 millionths), a little less that the theoretical, .00025" possible.
The height rise or depression in the bar's mid-point was only .000017", ( 17 millionths of an inch), a minuscule rise.
Height expansion of the front support was .000026", ( 26 millionths of an inch).
Height expansion of the rear support was .000015", ( 15 millionths of an inch).
Side to side deflection was so small as to not be seen on the electronic indicator's meter.
So, the height expansion differential of the supports, a paltry 11 millionths of an inch, is divided by 19.5", the length of the main bar, and we get a result of one-half millionth of an inch per inch. No effect on target could be measured from this at all. Assuming you have wisely designed your base so as to rest each of the ball bearing sets on a non-tapered tube surface, this tiny length expansion will not change the way your scope is pointed or iron sights are pointed so there are no effects here at all. The only possible effect could come from a rise or depression in the middle of the main bar. So let's be really cautious and conservative here and say you got hold of a really bad piece of aluminum for the main bar which was .50" X 1.50" X 19.5", our bar's dimensions. Let's assume that it had four times as much deflection as our test showed in the middle of the bar.
Using these worst case numbers, we find that the worst aiming error you could possibly expect at 100 yards is a tiny .025", (twenty-five thousandths of an inch). Remember, our actual test results would only support one-fourth of that number, a paltry 6 thousandths of an inch. Hard to measure that effect when the winds can blow your bullet off target by whole inches!
Do the math yourself. 4 X 17 millionths is 68 millionths. That is the height of your right angle triangle. The base dimension of the triangle is 19.5" divided by 2 or 9.75". So, to find the deflection of your scope reticle at 100 yards we do a basic proportion formula. This is the one we always use, so we don't get confused.
The height is to the base dim. as X is to the number of inches in 100 yards or 3600"
.000068" : 9.75" = X : 3600"
This ratio formula is always solved this way: factor 1 x factor 4 divided by factor 2 = X, so we calculate it like this:
.000068" x 3600" = .2448" divided by 9.75" = X
X = .025"
Frankly, this result doesn't even register on our "Oh Crap-O-Meter" which accurately measures real problems we encounter in the shop every day.
Incidentally, less technical questions can be answered by much less blather!!
Best Regards,
Tracy and Mike