Napoleonic Wargame Club (NWC)

I have been thinking about blitz tactics, columns vs line, and musketry (since it is more fun than building a resume), and started wondering just what the flight of a musket ball was. So here are my results, given certain assumptions:
1) Muzzle velocity of 800 fps (average of 700-900 found on the web).
2) Drag proportional to v**2 only (ie musket ball aerodynamic enough so that lower order terms are significant only after ball is 'spent').
3) Drag coefficient should result in a spent ball, travelling at 400 fps at a distance of 1050 feet (350 yds), the distance frequently referred to as maximum range for a musket.
4) For low angles of elevation we will have cos theta >> sin theta, so the vertical component of velocity can be ignored for purposes of calculating drag.

Using Excel (since that is easier than integral calculus) with a delta-t of 0.05s, I discover that the equation
v(t+0.05) = v(t) - 0.0000325 * (v(t)**2)
satisfies my assumptions.

Now charting two seconds of flight for elevation angles of -0.05 degrees to 0.40 degrees, produces some interestsing results. In the kill zone of 2.5 - 5.0 ft above ground level, and assuming further:
5) That balls much more than 5 feet high are unimpeded,; and
6) That the training to 'level' rather than 'aim' muskets combined with their vertical kick produces a roughly even spread of firing elevations.
then the density of musket balls out past 200 yds is constant! In fact the density is slightly higher out at 100-200 yds than it is closer in.

Image:


Due to it's low muzzle velocity, the path of musket fire resembles that of a long-bow much more than it does a modern high-velocity rifle. What this means is that volley-firing units do not fire at a target, but rather project a fire zone forward, not unlike a modern machine gun. Everything in front of the unit, out to effective musket range, suffers casualties at an almost constant rate regardless of intervening units.

In game terms, this means that when stacks of four 500 strength battalions approach a single battalion in line, and defensive fire occurs, every unit in the fire zone takes casualties approximately in proportion to its footprint on the ground. And every unit moving forward into that fire zone [edit: later in the turn] should be hazarding some degree of casualties.

That ought to slow down the blitz! No wonder commanders kept 200-300 yards (effective musket range) between the first, second and third battle lines.

Please note my 6 key assumptions listed above. I would be delighted to hear any comments that other members have.

Corollaries:

1) British troops were well-trained to (always!) level their muskets at the enemies knees. This will dramatically increase the number of musket balls in the fire range of 30-70 yds, while reducing to near nothing balls in the kill zone further away. No wonder they waited until seeing the 'whites of their eyes'. Don't bother volley-firing before the enemy advances to melee however; it's just a waste of powder and ammunition.

2) What of the morale boost for troops waiting 300 or so yards out in the second line, being hit from time to time by spent musket balls that cannot penetrate the uniform?

Any others?

Interesting. Now, 2 questions:
1) I don't suppose you have a similar chart for rifle fire, or is that too broad given the number of different rifles when considering the British Baker rifle vs all the various Prussian rifles?
2) Have you compared your chart to actual casualty results in any of the games (Talonsoft or HPS), to see if the results are what would be expected base on your analysis?

_________________
2nd Lieutenant Willie Davis
Light Bn Luneburg

After leaving the muzzle, the only difference between a musket ball and a rifle-fired projectile are as follows:

1) Possibly a different muzzle velocity, lower as I understand it during the Napoleonic wars because the same powder load was used but spinning the 'load' consumed part of the energy that in the case of a musket load was translational kinetic energy. (Can anyone out there provide a source for the muzzle velocity of the rifle used by Napoleonic-era troops?) A slightly lower muzzle velocity only has the effect of increasing the arc of trajectory slightly.

2) The spin of the bullet results in less of a knuckle-ball effect, allowing for better accuracy of aimed fire at short to medium range. The low muzzle velocity would have precluded any significant accuracy at long range, above about 200 or 250 yards, especially in the absence of a well understood science of ballistics being available to the common soldier.

3) Possibly a different 'load' shape; however my understanding is that rifles of this era continued to use balls rather than true bullets as we now know [edit - them]. A better shaped projectile would considerably extend maximum range, by decreasing drag, but would probably have less effect on the effective range of aimed fire, for the reasons stated above.

As for comparing my results to the HPS and BG games, my point is the following. With data of the time clearly showing that only about 1% of all issued small-arms ammunition generating casualties, there is a tremendous quantity of lead flying around in front of a battalion volley, out to several hundred yards, that is not being blocked in any way by the front line of opposing troops. If there are any other troops in that zone, they are going to take casualties in proportion to their footprint on the ground, because of the trajectory of low-velocity firearms and the manner in which troops were deployed. So when a 2000 man stack is fired on at 50 yards, it will be suffering 5 times as many casualties as when a 400 man stack is fired on in the same circumstance. If there is a second 2000 man stack right behind, at 150 yards, it will also be taking the nearly same casualties as the first stack. This is a simple consequence of the physics involved.

However, the casualties suffered by a 500 man unit of three-rank troops will be between 2/3 and 1/2 (depending on how you calculate the porosity of the first rank) those suffered by a 500 man unit two-rank troops in the same formation.

These are non-intuitive results, only become clear upon a close examination of the physics involved, and have not been accurately modeled in any set of Napoleonic war-gaming rules that I am aware of.

Pieter,

the trajectories you show in the first post are far too steep. Apparently muskets were not fired at such an angle. After all they were leveled, not set at 60 degrees with horizon. I'm pretty sure the effect you are talking about didn't take place. Also take notice of the bullet velocity when it falls almost vertically. It must be much lower than initial muzzle velocity - hence much less effect. And the last point, the tracetory must not bend is such an "s" shape at it's end. It's simply impossible and should be corrected.

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Note that the x-axis is in yards, 25 yards per major division, and the vertical axis is measured in feet, 2.5 feet per major division. This produces a clearer picture of the individual tracks, though it does exagerate the vertical angles very considerably.

Could you post here the whole spreadsheet with computations, please?

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I cannot upload a spreadsheet to the board. If you email me offline I will email it to you.

The s-bend at the end was due to putting a
max(0,...)
on each formula. By removing this and allowing negative heights the curve-fitting algorithm works much better. - I've only known for thirty years how to do this correctly.