Impact Testing using a Carbon Paper Sandwich - James Prescott

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Impact Testing using a Carbon Paper Sandwich (Simple Part)

Copyright © 1996, 1997 James Prescott

This process is useful for anyone testing a new blunt design. It helps identify possible concerns prior to live testing on human volunteers.

For example, if we had used it 10 years ago while developing the Montengarde blunt, we would have discovered that they have a "hot spot" in the centre. The blunts could have been redesigned.

1	Cut a sheet of plastic 8.5 X 11 inches. An ordinary plastic shopping bag will do fine.
2	Take the plastic, then a sheet of plain paper, then a sheet of carbon paper (messy side away from the plastic), a second sheet of plain paper onto which the impressions will be made, and finally a piece of artist's illustration board or equivalent (thick soft non-corrugated carboard). Tape this sandwich to a concrete wall with duct tape. The plain paper should be next to the wall.
3	Fire some arrows (I suggest about 6) at the carbon paper sandwich, attempting to hit different parts of the target with each shot. I fire from a range of about 10 feet, from behind a pavise, wearing my combat archery helmet and gloves.
4	Remove the sandwich from the wall, and label the paper that has the impressions with the date, type of blunt being tested, and any other useful information.
5	Do a series of comparison shoots with known blunts. You will be able to shoot a number of tests using the same sheet of carbon paper before it wears out.

At this stage, eyeballing the marks made on the various sheets of paper will probably tell you all you need to know. Try it with a few of your favourite blunts, and you'll see what I mean.

That's all most testers will ever need to do. For the more persnickety, check out the "Mathematical Part" of this note.

End of Simple Part

Impact Testing using a Carbon Paper Sandwich (Mathematical Part)

Copyright © 1996, 1997 James Prescott

For instructions on how to construct and use a carbon paper sandwich, check out the "Simple Part" of this note.

Here is where you come if you need a more sophisticated analysis of your results than you can get by eyeballing the impact marks.

Quantitative Measurements

If you need a mathematical analysis, here are some details of what I did.

In order to compare different blunts, make sure that the marks are all made using similar carbon paper.

6	Measure the diameter of each impact mark, and write it next to the mark. If the mark has different regions, such as a darker centre section and a lighter outer section, measure both. The edges will be indistinct, so make a best estimate. If in doubt, make several measurements. Calculate an average diameter for each distinct region made by the blunt being tested. Most blunts will make marks with only one or two distinct regions.
7	Obtain a density scale. Professional density scales can be obtained from photography shops. If you have a professional densitometer, even better. I made an adequate substitute at home in a few minutes on my computer using Clarisworks. I made a ten inch long rectangle filled with a 0-100% density gradient. I added bars and labels every inch, and then printed it on my LaserWriter. The result looked something like this: ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ >> \| . .\|....\| : :\|::::\| + +\|++++\| * \|**\| @ @\|@@@@\| << trim \|. . \|....\|: : \|::::\|+ + \|++++\| * \|***\|@ @ \|@@@@\| \| . .\|....\| : :\|::::\| + +\|++++\| \|**\| @ @\|@@@@\| \|. . \|....\|: : \|::::\|+ + \|++++\| * \|****\|@ @ \|@@@@\| \|____\|____\|____\|____\|____\|____\|____\|____\|____\|____\| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Trim the paper along the line >> ... << so that the density gradient runs right out to the edge of the paper.
8	For each distinct region within each mark, try to match the darkness of the mark with the density of some part of your density scale. Write the number for each region down next to the mark. Since the density within each region will vary widely, make a best estimate. I found it helpful to slightly unfocus my eyes. At the beginning, it will seem a very subjective process. With an hour or so of practice it becomes quite a bit more objective. After an hour or so you might want to go back and check your first measurements, and adjust them if necessary. Calculate an average density for each distinct region of the blunt being tested. If you are using your own computer-printed density scale, the density percentages will of course not be absolute.

Quantitative Analysis

The following analysis is just an example of one line of reasoning that might be followed given the raw data collected above. Many other lines of reasoning are possible.

The numbers for the example are taken from the tests I did at the end of November 1996 (and at subsequent dates).

Write down the highest average density for each type of blunt.

Since bruising is caused by pressure generated within flesh, and since the density of carbon paper sandwich impact marks is probably related to the pressure that the blunt applies to the wall, there may be a valid relationship here.

If there is, then the most intense bruise would be related to the darkest impact mark.

For example, in a series of tests I did, the highest average densities were:

	Baldar #2 & #4 (blue)	22 %
	Baldar #10 & #11 (yellow)	25 %
	Morak	54 %
	Saunders	55 %
	Thistle	65 %
	Film canister	68 %
	Baldar #3 (black)	70 %
	Montengarde Mark I	78 %
	Montengarde Mark II	78 %

If your concern, as a marshal, is to limit the intensity of possible bruising, then you could say that if the Montengarde blunt is considered acceptable, then all of the other blunts in this series of tests are also acceptable.

While the intensity of a bruise may be related to the highest pressure generated by the impact of a blunt, the size of the initial bruise is also important.

Calculate the average area of each region within an impact mark, and multiply by the average density of that region. Add all regions together for each blunt.

This may give an approximation of the intensity of an impact, times the area of that intensity.

For example, the blue Baldar blunt had a darker centre region with an average diameter (d) of 20 millimetres, and an average density (n) of 22%. The product of area times density is (we ignore constant factors like pi) d * d * n, or 8800 arbitrary units.

For the lighter outer region, with average diameter (D) of 34 millimetres and average density (N) of 12%, the product is ((D * D) - (d * d)) * N, or 9072 arbitrary units.

The sum for both regions for the blue Baldar blunt is 17872 arbitrary units. Similarly:

	Saunders	15248 arbitrary units
	Montengarde Mark I	17792
	Baldar #2 & #4 (blue)	17872
	Morak	20088
	Baldar #10 & #11 (yellow)	25175
	Thistle	25261
	Montengarde Mark II	25770
	Baldar #3 (black)	37030
	Film canister	55800

In order to compare these directly with the numbers from step 9 above, force the highest value in this step to be the same as the highest value from step 9. This is called "normalisation". In this example, force a high value of 78 by dividing by 715.

	Saunders	21 arbitrary units
	Montengarde Mark I	25
	Baldar #2 & #4 (blue)	25
	Morak	28
	Baldar #10 & #11 (yellow)	35
	Thistle	35
	Montengarde Mark II	36
	Baldar #3 (black)	52
	Film canister	78

If your concern, as a marshal, is to limit the total amount of possible bruising, then you could say that if the Montengarde blunt is considered acceptable, then the black Baldar blunt (at 44% higher) is probably not, and the film canister is definitely not.

Since I personally think that the intensity of bruising and the total amount of bruising are both important, I then arbitrarily averaged the results from steps 9 and 10.

	Baldar #2 & #4 (blue)	24 arbitrary units
	Baldar #10 & #11 (yellow)	30
	Saunders	38
	Morak	41
	Thistle	50
	Montengarde Mark I	52
	Montengarde Mark II	57
	Baldar #3 (black)	61
	Film canister	73

If you agreed with my preferences, then as a marshal you might say that if the Montengarde blunt is considered acceptable, then the black Baldar blunt (at 7% higher) is probably not significantly worse. It would probably be acceptable, particularly if it could be made a bit softer. And the film canister (at 28% higher) would probably be unacceptable.

The ratio between the values for the Saunders blunt and the two Montengarde blunts (averaged), all of which are made from very similar polyurethane, is in excellent agreement with the theoretical dependence of bruising on the inverse of the impact area.

Caution:

These values will *not*, repeat *not*, be directly comparable to values measured by other marshals. They offer a relative comparison only, within the set of blunts measured by one marshal.

Notes on the blunts:

The blue and black Baldar blunts were prototypes. The yellow Baldar blunt is an approved 6/4 inch blunt (the first one, not the later "egg" Baldar). The Saunders is the original approved 7/8 inch blunt from the early days of SCA combat archery. The Morak and Thistle blunts are approved 5/4 inch blunts. The Montengarde blunts are approved 3/4 inch blunts. The film canister was a prototype 5/4 inch blunt.

End of Mathematical Part

Yeoman Master Thorvald Grimsson

Carbon Paper Sandwich Empirical Tests

Copyright © 2001, 2004 James Prescott

First empirical test

I decided to do some quick carbon paper sandwich tests comparing arrows and crossbow bolts, even though my bow and crossbow don't exactly match. The bow is about 495 inch pounds at full draw, and the crossbow is about 520 inch pounds.

The marks made on the paper during this test do not necessarily correspond in size and intensity to the bruises that would be caused in human flesh. However, I believe that they probably give a first order indication, which I call bruising potential.

I tested eight different combinations:

Baldar on wood shaft arrow
Baldar on wood shaft crossbow bolt
Baldar on fibreglass shaft arrow
Baldar on fibreglass shaft crossbow bolt
Morak (with added foam) on wood shaft arrow
Morak (with added foam) on wood shaft crossbow bolt
Morak (with added foam) on fibreglass shaft arrow
Morak (with added foam) on fibreglass shaft crossbow bolt

Note that this is the original pattern Baldar, not the later "egg" Baldar.

First, I eyeballed the impact marks (see Simple Part above).

By eyeball, there is _not_ an obvious difference among the four Baldar equipped missiles.

By eyeball, there is _not_ an obvious difference among the four Morak (with added foam) equipped missiles.

The eyeballing suggests that arrow versus crossbow bolt makes no difference.

The eyeballing suggests that wood shaft versus fibreglass shaft makes no difference.

Second, I made some measurements of the areas and densities of the impact marks, treating each distinct ring separately (see Mathematical Part above).

Then, using a spreadsheet I summed the concentric areas times densities to get an approximate estimated bruising potential (corresponding to Steps 10 and 11 of the Mathematical Part above).

I then included missile masses and inch pound measurements for the bow and crossbow; and calculated relative kinetic energies and relative velocities. I then explored a number of possible relationships.

The average inch-pound rating for the bow, corrected for the actual draw length for each arrow, was 457. The inch-pound rating for the crossbow was 520.

The calculations confirm that kinetic energy per unit area is the best theoretical predictor of bruising potential for similar blunts.

If we plot the ratio of bruising potential over kinetic energy per unit area (which we will call the specific bruising potential, we find that for the Morak blunts with added foam the ratio is constant with a standard deviation of 13%, and for the Baldar blunts the ratio is constant with a standard deviation of 9%.

The calculations show that arrow versus crossbow bolt makes no significant difference.

The ratio of the specific bruising potential for the arrows to the specific bruising potential for the crossbow bolts is 1.12 with a standard deviation of 16% (which says that these arrows are 'hotter' than these crossbow bolts, but not by a significant amount).

The calculations show that the addition of half an inch of uncompressed closed cell foam does significantly reduce bruising potential.

The Morak without added foam had a bruising potential of 41 (see step 11 of the Mathematical Part above), and the Morak with added foam has a significantly reduced bruising potential of 30, equal to that of the Baldar blunt. It is interesting to note that the An Tir decision to require the addition of closed cell foam to the Morak blunt seems to have been almost exactly on the money if the intent was to make it equivalent in impact to the Baldar blunt. This could be considered an indirect validation of the Carbon Paper Sandwich method.

The data are not precise enough to permit other conclusions, though there is an intriguing hint that the Baldar on wood shaft combination may have a bruising potential about 8% higher than the Baldar on fibreglass shaft combination, despite the Baldar on fibreglass shaft having a higher kinetic energy.

Further investigation is indicated.

If the difference turns out to be 8% or less, that would not be significant, and would probably not be detectable in the field. If the difference turns out to be over 8%, it might become detectable in the field.

It should be noted that other historically acceptable SCA blunts have a bruising potential significantly higher than the Baldar. Even if the Baldar on wood shaft combination turns out to have a higher bruising potential than the Baldar on fibreglass shaft combination, the result will still lie well within the range of historically acceptable bruising potentials.

It is tempting to speculate whether this difference, if it turns out to be real, might be related to the 'jackhammer' behaviour previously noted for wood shafts used in conjunction with Baldar blunts. The 'jackhammer' behaviour is a longitudinal resonance effect in wood arrow shafts, triggered by the deceleration impulse on impact, and does not necessarily occur with other blunt and shaft combinations.

In conclusion:

The data show that with respect to bruising potential there is no significant difference between arrows and crossbow bolts.

The data suggest that with respect to bruising potential there is no significant difference between wood shafts and fibreglass shafts.

Second empirical test

John Edgerton (Sir Jon Fitz-Rauf) did some actual on-the-flesh tests comparing Baldar blunts and Thistle blunts (5 shots each from ten yards, through light padding).

"At this point the marks were about the same, both in size and redness, with two of the Thistle marks being a little redder with a more noticable outer circle.

"After an hour they seemed to haved peaked in color, with the two Thistles still slightly redder. The red areas from both sets had slightly increased in size.

"After the second hour they all began to fade out. After six hours thye would have been very hard to find if not for the ink marks showing their location. The same two Thistle impacts were slighty less faded(they were over my ribs on the lower left side.

"By morning, eleven hours later they were gone." (personal communication 1997-January-13)

The description of the marks as being similar in size and redness, with a slight additional redness for two of the Thistle impacts which were over ribs, suggests that the field-measured bruising potentials could be similar, with the Thistle being perhaps slightly higher.

The integrated area/density values from my carbon paper sandwich tests (against cement) have the Baldar and Thistle identical at 35 each. The maximum density values are much higher for the Thistle, and are concentrated at the outer edge of the impression, which matches the "more noticeable outer circle" that Sir Jon reports.

The way I read it, there is excellent agreement between the Carbon Paper Sandwich method results, and these live on-the-flesh tests.

Third empirical test

Bob Curtice (Master Robert of Vinhold) suggested in 1998 dropping missiles onto a carbon paper sandwich on the floor, adjusting the mass of the missile and the height of the drop so as to get a similar kinetic energy as the same missile fired from a bow or crossbow. These would be low velocity / high mass impacts, as opposed to the high velocity / low mass impacts from a bow or crossbow.

I took a Montengarde Mark II blunt, which happens to be at the limits of historically acceptable bruising, and for which I have a set of impact impressions made by such a blunt when fired from a bow, so that a direct comparison of impressions would be possible.

I made a crossbow bolt of exactly the right length so that if I held the nock against the ceiling of the room, the Mark II blunt had exactly six feet to fall to the concrete floor. Ignoring drag, which we can do, this means that the arrow will be travelling at almost exactly 6.0 m/s when it hits the floor.

The wood arrow fired from a 30 pound bow has a mass of 0.037 kg, velocity of 37.4 m/s, and an impact diameter of 0.75 inches. The test bolt with a velocity of 6.0 m/s needs to have a mass of 1.45 kg (3 lb 3 oz) to have the same kinetic energy. A package of cold chisels plus enough fibre tape to tape them securely to the crossbow bolt makes a crossbow bolt of the desired mass.

To get a clean impact without the crossbow bolt skidding to the side after impact required that I rig a guide tube. Even with the guide tube, four out of ten impressions had to be rejected for excessive skid. Two of the ten impressions were so anomalously light that they had to be rejected. Perhaps because the guide tube had somehow interfered with the drop. The crossbow bolt bounced a number of times, leaving secondary impressions. These secondary impressions were obvious, and were ignored.

I compared the four remaining valid impressions with the 19 impressions created by firing the arrow from the bow.

The bow impressions all have a very distinctive 'hot spot' in the centre. This is largely absent from the dropped impressions, which merely have a rather broad region of higher density over most of the centre of the impression.

The bow impressions average 24.2 mm in diameter. The dropped impressions average 21.5 mm in diameter. This is a significant difference. Clearly the 'squidging' outwards that occurs for bow impressions is not happening for the dropped impressions.

The maximum density in the centre of the dropped impressions ranged from about 65% to over 100%. This is a significantly greater variance than occurred for a typical bow impression for any blunt. Taking the impression whose maximum density was off-scale as 110% (estimated), the average maximum density was 82%. This is close to the average for bow impressions for Montengarde blunts which was 78%. However, in view of the many significant differences between the two sorts of impressions I am inclined to consider that this may be a coincidence.

The overall appearance of the dropped impressions is darker than the bow impressions.

I make two observations.

First, the behaviour of this design of dropped bolt is quite inconsistent, and can readily be upset by the use of the guide tubes, skidding, and bounces.

Second, there are clearly significant differences in the dynamics of impact for a low mass / high velocity object and a high mass / low velocity object.

I draw one tentative conclusion.

Weighted dropped crossbow bolts may not be a suitable method for testing impact using the Carbon Paper Sandwich method.

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