Bruising and SCA Missile Combat - James Prescott and Gary Renshaw |
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Bruising and SCA Missile CombatCopyright © 1987,1997 James Prescott and Gary RenshawThis article examines some theoretical aspects of missiles and bruising in the Society for Creative Anachronism (SCA), and examines grounds for setting a maximum mass for javelins. This article makes the following chain of assumptions:
The MissilesWe use two actual war arrows (19 mm minimum flat frontal diameter), and five imaginary javelins (51 mm minimum flat frontal diameter). A light SCA war arrow (0.030 kg) shot from a good modern recurve bow with 31.2 J of energy available. 80% efficiency is typical for such a combination of bow and arrow. This gives an initial velocity of 40.8 m/s. A heavy SCA war arrow (0.049 kg) shot from the same bow. Assuming a constant effective mass for the bow, the heavier arrow will be shot with an efficiency of 87%. This gives an initial velocity of 33.2 m/s. A javelin with the mass of a baseball (0.145 kg). The world record distance for a thrown baseball is 138 m (Guiness Book of Records). We can use elementary physics to calculate an initial velocity of 37 m/s. Three javelins based on hand grenades (0.4, 0.6 and 0.8 kg). The grenades have ranges of 46, 37 and 32 m (Intelligence Bulletin, U.S. War Department, June 1946). We can use elementary physics to calculate initial velocities of 21, 19 and 18 m/s. A javelin with the mass of a brick (2.27 kg). The world record distance for a thrown brick is 45 m (Guiness Book of Records). We can use elementary physics to calculate an initial velocity of 21 m/s. If we assume that the baseball and the brick are thrown by the same person, we can calculate that the effective mass for the arm is about 0.9 kg and that the energy available is about 690 J. If we assume that the hand grenades are all thrown by the same soldier, we can calculate that the energy available is about 280 J. Research done by the first author some years ago indicated that the ratio between the energy available for a world record and the energy available for a normal maximum effort (by men or horses in excellent condition) was very close to two to one. It is therefore reasonable to assume that an SCA fighter does not have more than 350 J of energy available for throwing. We now introduce what we call the SCA javelin equation which relates mass and velocity for javelins: one half (mass plus 0.9) times velocity squared equals 350. Using this equation we re-calculate initial velocities for the five imaginary javelins of 26, 23, 21.5, 20 and 15 m/s. Note that armour worn on the arm would increase the effective mass of the arm and thus reduce the initial velocity of the javelin. The Mathematical ModelsAll models assume that bruising is inversely proportional in some way to the size of the face ('presenting surface') of the missile. The kinetic energy model (KE) assumes that bruising is proportional to the kinetic energy of the missile (mass times velocity squared divided by diameter squared). Note that for bullets that actually penetrate the body, damage is generally reckoned to be proportional to the amount of kinetic energy ('striking power') transferred from the bullet to the body (Calgary Medical Examiner's Office). The momentum model (MOM) assumes that bruising is proportional to the momentum of the missile (mass times velocity divided by diameter squared). Note that this model is the one that we feel is least likely to be realistic. The midway model (MID) is midway between kinetic energy and momentum (mass times (velocity raised to the power 1.5) divided by diameter squared). The pressure model (PRE) assumes that bruising is proportional to the pressure generated in the flesh ((square root of mass) times velocity divided by diameter). For four contrasting models, we turn to the impact of naval shells on naval armour plate (Nathun Okun, Warships International, 1976-1980). All four models were empirically determined, and each is valid for some range of thickness ratios (the ratio of the thickness of the armour plate to the missile diameter). In all four models damage is assumed to be proportional to the depth of penetration. For thickness ratios below 0.025, the shell dishes the armour over a wide area (NAV1). Depth of penetration is proportional to ((square root of mass) times velocity divided by diameter). This is the same formula as the PRE model. For thickness ratios between 0.1 and 0.33, the shell bends the armour sharply over a small area (petalling) (NAV2). Depth of penetration is proportional to ((square root of mass) times (velocity raised to the power 1.5) divided by (diameter raised to the power 1.5)). If the missile is flat-nosed (NAV3), the depth of penetration becomes proportional to ((square root of mass) times (velocity raised to the power 0.75) divided by (diameter raised to the power 1.8)). Note that these two models, which describe bending the armour sharply over a small area, seems to match best the initial physical appearance of bruises. For thickness ratios greater than 0.82, the shell splashes the metal at the surface and then tunnels through the metal as if it were a liquid, pushing the metal sideways out of the way (NAV4). Depth of penetration is proportional to (mass times velocity squared divided by diameter squared). This is the same as the KE model. Normalized Relative DamageThe following table shows the relative damage predicted by each model for the seven missiles. All figures have been normalized so that for each model the more damaging arrow (which, remember, is assumed to be acceptable) is made to equal 100. A javelin with a relative damage of over 100 according to a model would be unacceptable if that model were a valid predictor of the intensity of bruising.
Maximum Acceptable Javelin Mass (in kg)The following table shows for each model the calculated maximum acceptable javelin mass, which is the mass that would have a predicted relative damage of 100. The first case assumes that 690 J of energy is available (world record holder). The second case matches the table above, and assumes 350 J (SCA javelin equation). The third case assumes 280 J (average soldier). In each case the relative damage predicted by the NAV2 model never reaches 100.
Discussion and ConclusionFour of the models suggest limits on the mass of javelins, based on the SCA javelin equation, ranging from 0.5 kg (1.1 pounds) to 1.1 kg (2.4 pounds), and two suggest that no limit is needed. In the absence of a clear indication of which model of bruising is accurate it would not be possible to choose conclusively among the models. We suggest a limit of 0.9 kg (2 pounds) for javelins (and other thrown weapons) on three grounds. Firstly, on the grounds of authenticity a limit of about 0.9 kg is reasonable, for the Olympic javelin has a mass of 0.8 kg, and a typical francisca (Frankish throwing axe) had a mass of 1.2 kg. Secondly, a limit of 0.9 kg would avoid undue strain on the throwing arm by matching the mass of the javelin to the effective mass of the throwing arm (which is about 0.9 kg). Lastly, our purely intuitive feeling based on inspection of the above tables is that 0.9 kg is the most probable value for the theoretical limit. Supporting CommentaryIn a September 1987 letter of comment on this paper, for which we wish to express our profound thanks, Dr. M. R. Yeadon of the Biomechanics Laboratory at the University of Calgary makes several observations. Firstly, Dr. Yeadon suggests that "the intensity of bruising is an increasing function of the depth of depression" of the tissue, and derives a relationship based on the reaction force of the tissue. Secondly, Dr. Yeadon points out that "while this relationship is not explicit we do know that a given level of bruising is associated with a particular value of" kinetic energy divided by the area of contact (that is, the KE model). Thirdly, Dr. Yeadon cites "elite performances of 0.8 kg javelin throwing [for which] the speed of release is close to 30 m/s", giving a kinetic energy for the javelin of 360 J. Fourthly, Dr. Yeadon agrees that "our typical spear thrower" would give the javelin half that energy, or 180 J. Fifthly, Dr. Yeadon calculates bruising intensities for this javelin and for the heavy SCA war arrow (for purposes of comparison with the first table above, the calculated intensities may be normalized to 71 and 100, respectively). Dr. Yeadon concludes: "Even assuming that a 1.0 kg spear can be thrown at the same speed, the bruising intensity will be close to that of a heavy war arrow. A 1.0 kg limit on spear mass is appropriate."
Yeoman Master Thorvald Grimsson
Montengarde, An Tir
[ The original article had an error in the energy available in the good modern recurve bow. The article has been corrected to match. ] |
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