## Sharp Shooter Maths

May 14, 2010

Mathspig grew up on a police station in the small Australian country town of Kyneton, Victoria in the 1960s. Mum fed the prisoners. Dad’s car an old FC Holden, maroon and white with a pink door, was the police car. And the police phone sat in the kitchen.

Australia has a very strict gun laws today. Thank goodness. But such laws didn’t exist in the sixties. My Dad’s .22 rifle rested against the fridge in the kitchen – without it’s 6-bullet magazine – in case my dad was called out to some police emergency.

There were a number of gun incidents in my childhood. One time my mum was cleaning the house. She usually put paper rubbish in her apron pocket and threw it at the end of the day into our combustion (wood-fired) stove. She forgot she had three .22 bullets in her pocket. It took some time for the bulletsto heat up.

My parents were in bed when bullets started exploding in the kitchen. The explosion blew off the hot plate and blew the ash door open covering our kitchen in grey ash. And it nearly gave my dad a heart attack. This was a typical story of my childhood and why I became a humour writer.

My Dad the Sharp Shooter My dad stopped a stolen car with one bullet. This was considered legendary by his fellow cops. He didn’t shoot the tyres. He managed, by accident and possibly even though he was aiming at the tyres, to hit the electrical lead into the car’s  distributor cap. Phht! Car go no more.

Sharp Shooter Maths

One measure of the accuracy of rifles, riflescopes but also the sharpshooter is the MOA or Minute of Angle.  The MOA can also be used to define the target zone (circle).

I cannot show you a triangle with an angle of 1′ because it would have to be 100m long on one side and only 3cm tall or 100 yds long and approx 1 inch tall.

Needless to say, drawings are NOT to scale.

A sharpshooter can put 5 out of 6 bullets in a target zone drawn at 1′ angle around centre of target at any distance.

(See pics. )

As the distance away from the target increases the target zone circle area increases.

When Mathspig recently saw images of some Russian soldiers covered in medals it prompted the question ‘Would medals protect the wearer from a sharpshooter?’ Note: Mathspig has obscured the identities. This is a theoretical maths question.

Mathspig was interested in this question because megalomaniac military dictators who take over countries by force tend to award themselves lots of medals. But they are also likely to be the target of sharpshooters from a liberation movement.

The diameter of a standard military medal is 3.5 cm. Mathspig has drawn up a diagram with loosely packed medals.

Using Pythagorus Theorem we can calculate the distance ac and then by subtracting 2r (2 x radius of the medals) we end up with the diameter n of the target zone circle.

Even at 100m the sharpshooter is looking at a target zone circle with a radius of 0.46cm. That is less half cm!!!!!!! The target zone is less than the size of an American Quarter and about the size of an Australian 10 cent coin or a British Pound. This is very difficult.

At 100m the sharpshooter is doing well to hit target in a target zone circle of 2.91 cm.

At 200m the target zone circle radius is 5.81 cm.

So the megolmaniac military dictator wins!!! He IS protected – on his chest – by his medals!!!!!! Unless the sharpshooter manages a ‘lucky’ shot.

Another way to look at the sharpshooter problem would be to calculate the MOA – or minute of angle- to get inside the target zone.  Here are the calcs for 200m. Find WEB 2.0 Scientific Calculator handy here.