Schlager Penetration Tests

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Test of Penetration Probability of an Untipped Schlager Blade

Through Three and Four Layers of Trigger Cloth by Robin of Gilwell / Jay Rudin

May 13, 2004

Abstract Tests were run comparing three and four layers of commercially available trigger cloth as protection from penetration by an untipped schlager blade. The tests showed with a p-value of .000641 that there was a significant difference. The mean with three layers was close to 40%, with a 95% confidence interval of ± 20%. No penetrations were seen with 4 layers of trigger cloth.

1. Introduction

I recently was inspired (thank you, Christian Fournier!) to add some mathematical rigor to our tests of armor.

This test was conducted very briefly and informally. I took my available 35” schlager blade, and some trigger cloth previously tested and accepted as armor by Ansteorran standards. I cannot give the source of either, since I’ve had both for ten years or so. The blade was originally provided by Christian Dore, at the time that he was the Heavy Rapier Marshal in Ansteorra.

I went outside with my untipped schlager blade and trigger cloth, and ran an experiment. All blows as identical as I could make them. The raw data is as shown:

4 layers of trigger cloth -- 0 penetrations in 20 tries.

3 layers of trigger cloth -- 9 penetrations in 22 tries.

All thrusts were delivered by Robin of Gilwell, attempting to give consistent thrusts significantly harder than the average blow received on the SCA fencing field, and only slightly harder than the hardest blow ever received.

2. Data Analysis

To test the null hypothesis that the penetration percentage is the same, against the alternate hypothesis that the penetration level of three layers is greater requires the following test:

Formula 1.PNG

The rejection region is z < -1.645 for a 5% significance level. In fact, at -3.22 standard deviations, the test has a p-value of 0.000641. This means that there is less than 1 chance in 1500 of achieving this result if the null hypothesis were true. It is therefore reasonable to reject the null hypothesis, even with only 42 points of data.

The 95% confidence interval for the probability of penetration with three layers is

Formula 2.PNG

(This is an approximate value, using a t-test with 21 degrees of freedom. To be more accurate, binomial expansion should be used.) Similarly, using a one-sided interval, we can state that there is a 95% confidence that the penetration proportion with three layers is

Formula 3.PNG

While I’ve calculated with 3 digits, I don’t believe that this method is that accurate, so the most we’re able to say is that we are 95% confident that the penetration proportion is between 19 and 63%, or that we are 95% confident that it is greater than 23%.

Of course a confidence interval that goes from 20% to 60% isn't very precise, and most studies worth hiring professionals for require far more precision. (I remember a certain amount of fuss and bother in Florida four years back about the imprecision when a certain statistical study gave results of 50.0% +/- .01%.) So if I were being paid for the trigger cloth study, I would collect many more data points and create a much smaller confidence interval. But the quick, sloppy study done is enough to indicate that an overly hard shot represented by my test thrusts probably gets through 3 layers more than 20% of the time.

The 95% confidence interval for 4 layers cannot be solved that way, because np is less than 5. By binomial expansion, however, it can be shown that if the population proportion (percent chance of penetration) were .15 or more, then there would be a less than 5% chance of the observed result.

Or, if you prefer, we can do a chi-squared test. Testing the hypothesis that number of layers of trigger and probability of penetration are not related, we calculate:

Formula 4.PNG

The 5% rejection region is Formula 5.PNG. The 0.5% rejection region with one degree of freedom is Formula 6.PNG. Clearly, the number of data points is sufficient to reject the null hypothesis that the probability of penetration is unrelated to the number of layers of trigger.

3. Limitations of the Study

Of course, there are many limitations to this study -- chief among them that I am imperfect, human, and in a hurry. I tried to arrange the layering so that I wouldn't know when it was three and when it was four layers, but I had a vague idea where the hidden fourth layer was. If I were getting paid consultant rates, the thrusts would have been mechanical, or done by someone who had no idea what was being tested.

Small data sets can be conclusive, depending on what level of precision is needed. For proportion data, a very rough 95% confidence interval can be produced by taking Formula 7.PNG. So if you have 25 points of data, the interval is plus or minus 1/5. With 100 points, you have plus or minus 10%. The reason that most studies use thousands of data points is that they want precise limits. A 2% spread requires roughly 2500 points, for instance. (Gross simplifications used here.)

Also, the thrusts were (deliberately) much harder than the average hit received on the SCA fencing field. While such hits do, in fact occur, they are quite rare. The odds of receiving one immediately after the tip came off and before the marshals stopped the fight is quite low. It is therefore not reasonable to assume that if a fencer were hit by an untipped schlager, it would have a 40% probability of penetrating three layers of trigger. It is, however, quite reasonable to assume that it would not penetrate four layers.

Finally, there are many fabrics sold as “trigger” these days. Just because it says “trigger” on the label does not mean that four layers of it is safe. The trigger cloth used in the study was previously tested to ensure suitability as SCA fencing armor.

4. Conclusions

So the rough conclusions are: 1. Two different tests show that the penetration probability with three layers is significantly more than the probability with for layers. 2. The mean penetration proportion with three layers of trigger cloth was 40.9%. No penetrations were observed with four layers. 2. We have a 95% confidence that the penetration proportion with three layers of trigger cloth is greater than 20%. 3. We have 95% confidence that the penetration proportion with four layers of trigger cloth is less than 15%.

Therefore, it is reasonable to assume that a grossly over-hard hit from a schlager is significantly more likely to penetrate three layers of trigger cloth, but far less likely to penetrate four layers

Robin of Gilwell

John Rudin, Ph.D. (Operations Research)

Lecturer, Statistics and Operations Research, University of Texas at Dallas.

Adjunct Professor and recent Area Chair for Statistics and Quantitative Methods, University of Phoenix

A.S.A.(1985-1989), M.A.A.A.(1985-1989)

Permission is hereby given to reproduce this paper for any SCA marshallate purposes, and to publish it in any SCA venue, as long as I am sent a copy at:

John Rudin

Rudin Analytics, LLC

7135 Vinland St.

Dallas, TX 75227-1829


I also request to be informed of any copy put online.