I want to practice my (air) pistol shooting stance and aiming and “dry-firing” in my office.

The target black is 60mm dia.. The live shooting distance is 10 m.

What size circle should I print out to accurately scale this for practice at 2 m?

Do you even understand the question? Bit of an odd one I know but STW can do this.

1/5th

Aim Small … Miss Small

So a 12 mm dia. circle will do it? Thank you – simple inverse proportion then!!

Derrrrrrr

Yep it’s linear. So bringing the distance in by (2/10) = 5 you make the circle 1/5 smaller diameter.

If you want to prove it you use can trigonometry. Your radius of the circle gives you an angle from parallel, given as tan(theta) = opposite/adjacent = 0.03/10 (radius / distance). Keep the same angle over a shorter distance tan(theta) = new radius / 2 m. tan(theta) is the same in both so 0.03/10 = new radius / 2 , so new radius is 0.006 m or 6 mm, diameter 12 mm.

Very comprehensive Konagirl! Ta.

ficky.

ficky.

Fair comment!

This can be shown from the concept of a solid angle. Which is the area divided by radius squared. It’s the projection of an Area onto the surface of a sphere. There are 4*pi*r*r steradians over the surface of the sphere of radius r (distance away from you) and the fraction of these in an area A is your solid angle. So for your circle with radius R = 0.06m and a distance r = 10m, the solid angle is 3.14*0.06*0.06/10*10 = 0.0001134 steradians (about one eleven millionth of the total of the 10m sphere). The same solid angle projection onto a sphere always scales as R/r. Five times closer means five times smaller.

The concept of solid angle also applies to cinema screens. My projector screen in about 3m away and has is about 1.5*2.5m. For a cinema, I can calculate which row to sit in to preserve the same projection. Hint: it’s not the front row!

https://en.m.wikipedia.org/wiki/Solid_angle

Sod it, we’re chucking all the proofs in.

You can do all teh fancy stuff if you like. but its 30 seconds with a ruler…

I once nearly got a maffs degree

Are all the factors affecting the accuracy of a gun linear? The effects of stance on initial aim and recoil movement are I think linear.  A ballistic arc isn’t linear, although it is repeatable. What about aerodynamic turbulence – is that more random?

If not all linear, the weighting of the shooter’s stance within the total accuracy will not be constant, and scaling the target size linearly will not represent the accuracy obtained at a longer range.