Calculate distance for degree of angle

[Frank Malone]

Why don't I get the same calculated feet for the following degrees using
different ways to calculate when I get 1.047 inches at 300 feet using both
formulas for 1 minute deg angle. Which I feel sure is the correct answer.

lens
distance ft dia. ft circumference ft deg ft for 1 deg.
degrees calculated ft
10 20 62.83185307 360 0.1745329252
64.5 11.25737
10 20 " 360 "
23.333 4.072377
10 20 " 360 "
45.5 7.941248
10 20 " 360 "
15.666 2.734233
300 600 1884.955592 360 5.2359877560
0.016667 0.087266 x 12 = 1.047 inches for 1 minute of angle at 100 yds

Degrees Tan ft Calculated ft
64.5 2.0965435991 10 20.96544 Note above cal.
on 11.25737 ft
23.333 0.4313509937 10 4.31351
45.5 1.0176073930 10 10.17607
15.66 0.2804471323 10 2.804471
0.0166667 0.0002908882 300 0.087266 x 12 = 1.047198
inches

Can someone tell me what the correct formula is or what I am doing wrong? I
really don't understand why I get 1.047" for 1 minute of angle at 100 yds
which I have seen a lot of articles saying that's the correct for 100 yds.
I'm doing something wrong but can't figure out what.

 

[Tom Ogilvy]

A B C D
Deg Tan Dia Ft Calc in
0.016666667 0.000290888 300 1.047197581
15.666 0.280447132 10 33.65365588
45.5 1.017607393 10 122.1128872
23.3 0.43066804 10 51.68016476

=Tan(A*pi()/180)*C*12 for inches, drop the 12 for feet

Since you don't show your formula, it is hard to say. Anyway, my results
agree with your bottom table.

 

[Frank Malone]

I used this formula for top table. Distance 10 ft, dia. 20 ft x PI =
62.83158307/360 = .1745329252 x 64.5 deg. = 11.25737 ft for 10 ft from
camera lens.

Deg 10 Ft
64.5 11.25737
45.5 7.941248
23.333 4.072377
15.666 2.734233
0.0166667 .087266 this cal is for 300 ft for 1 min of angle (1/60=.016667
deg) which I feel sure is the correct answer. But I get the same answer
using Tan. Notice the big difference I get on 64.5 deg using circumference
and Tan 11.25737 and 20.965 so any help on what I'm doing wrong would sure
be appreciated.

 

[Tom Ogilvy]

Your approximating the circumference of the circle.

If I use you measure for a single degree, the formula becomes:

=TAN(1*PI()/180)*10*360

which equals: 62.8382337415833

If i use pi*2*radius for the circumference, I get:
62.8318530717959

When you use the tangent function, you are getting the length of the
opposite side for the right triangle formed by the angle in question. So
you are comparing the arc length of the angle to this measurement.