Introduction

I am constantly hearing people trying to claim that the schlager is just as safe as, or safer than, the epee. To me this is such an obviously false statement that I have never been able to argue with anyone effectively. I was unable to even begin to understand the logic someone might use to make such a claim. Then recently I was talking with a friend of mine who said something to the effect that the schlager is heavier, but it doesn't move as fast and that compensates. That is a perfectly reasonable misunderstanding. Maybe there are other people who have similar misconceptions. That is why I have taken the time to write up a simple mathematical proof of why, and by how much schlagers hit harder than epees.

Assumptions

In this argument I have made 7 simple assumptions.

1. The forces excerted by the human body on a schlager and an epee are the same.

2. The force used to accelerate the blade is constant for the entire time the blade is accelerated. I realise this is false however I do not believe adding a force curve to my calculations would change the results significantly.

3. No effort is made to slow the blade down, resulting in the blade making contact at its maximum velocity.

4.Contact is made at the tip as per a thrust. An epee blunt is the same size as a schlager blunt.

5. An epee and a schlager take the same time to stop after hitting the target.

6.The epee and schlager travel the same distance.

7.The shot is made under normal conditions and not those of extreme blade breakage.

Equations

I will be using a couple of simple physics equations in this calculation.

F is the force,  m is the mass and a is the acceleration.

P is momentum and t time.

V is the velocity.

A is the area.

and

respectivly.

Calculation

Calculating Pressure

What matters when one is trying to cause damage to the human body is pressure. People can take a lot of force so long as you spread it out over a large area. The pressure exerted by a blade on the body is defined by equation 6, where F is the force of impact of the blade, and A the area of the tip. So for a schlager,

and for an epee,

Here and throughout this calculation a subscript s indicates a variable for a schlager and a subscript e indicates a variable for an epee. I have also used assumption 4 in setting the tip areas to be the same.

Now expand these equations using equation 2 to get,

and

Here I am using the second form of equation 2 and using assumption 5. Here ΔP is the change in momentum. Since I have assumed the blade comes to a stop, all momentum will be lost and ΔP is the same as the maximum momentum, that is ΔP= Pmax. Resulting in

and

Now use equation 3 to arive at

and

Finaly define

Where μ is some arbitrary constant such that μ≥ 1. This finaly yields

and leaves the equation for unchanged.

Calculating Vmax

Equation 7 is the equation for velocity. Here t is the total time accelerating the blade, and a is the acceleration on the blade. So for an epee

Where is the force exerted by your body to accelerate the blade. Which implies

This yields

Now define

Now substitute 26 into 22 and get

Grouping terms results in

Now substitute using equation 17

Putting it all together

Now we are ready to substitute equations 28 and 30 into 16 and 18 which yields

and

Now simplify by grouping terms and get

and

Now to make everything clear notice that

Or expressed as a ratio

At this point I remind you of equation 17 which states This means that if your schlager is 4 times heavier than your epee it will cause 2 times as much damage. That would meen that you would need to have 2 times as much control to play schlager as to play epee assuming you wish to avoid hurting your sparing partner. I believe μ = 4 to be a very conservitive estimate, the real number being around 9-10. Which would imply that a person have 3 times as much control to play schlager as epee.