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Post by Mike Powell on May 6, 2007 14:31:55 GMT -6
How many times haven’t we wondered if the Indian advantage in numbers would be described by a linear or an exponential function? Of course it’s exponential, you scream, any dummy knows that! Well probably not GAC, since it appears the answer wasn’t understood until 1916. That year Commander Bradley Fiske, USN, published “The Navy As A Fighting Machine” containing a table illustrating numeric advantage doesn’t function linearly. www.gutenberg.org/files/17547/17547-h/17547-h.htm#chapter%20XIIRefer to Chapter XII “Operating The Machine” or take a look at the following chart showing results from 400 hostiles facing 200 hussars, everyone equally lethal with 2% of their shots.  Note we don’t end with a linear count of 200 dead hostiles when we’ve run out of hussars, only 55. The advantage ratio improves with every tick of the clock (actually round of fire), growing from 2 to 1 at the onset to a game ending 115 to 1. But what about actual numbers, terrain, tactics, lack of training, native hunting skill, carbine vs. Henry, etc.? Well and good, when all are factored together, an adjusted advantage ratio pops out. That ratio at the LBH? Unknown, but probably better than 1 to 1, in favor of the hostiles. And the point is the weaker side gets weaker exponentially as combat continues. Frederick Lanchester, automobile and aeronautical engineer and much more, improved Fiske’s tabular understanding around the end of The Great War by development of differential equations explaining attrition, yielding the coupled equation, drum roll and gasping nerds, AO^2-At^2 = B0^2-Bt^2. More of this “N-Squared Law” and its application to dreadnought battleship theory at www.navweaps.com/index_tech/tech-076.htm Lanchester is a darling of operations research and apparently his combat theories have been applied to, get this, marketing strategy by the Japanese. www.lanchester.com/I’m curious if any member with a military academy background may have seen “N-Squared Law” presented and what cautions are given about feeding weaker force on stronger? Perhaps GAC’s last words were, “Damn, if I’d only learned to do the math properly!” Yours, Mike Powell |
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Post by fred on May 6, 2007 16:06:33 GMT -6
Sorry Mike, no academy education here, but it doesn't take an academy education, drum rolls, gasping nerds, AO^2-At^2 = B0^2-Bt^2, or “N-Squared Law” to figure you don't want to attack a vastly superior force. That's why the Germans and the Americans-- and I sure, nowadays, everyone else-- likes the concept of concentrated force. Once you can impose your will on a specific sector, proper plans allow you to do much more. The Germans achieved vast successes in WWII and we did the same in Vietnam. I do not recall a single operation we were involved in where we knew we had an advantage in numbers. We won our battles w/ weaponry, not factored in your table.
Custer had no such distinct advantage, thus your presentation makes eminent sense.
Best wishes,
Fred.
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Post by mcaryf on May 6, 2007 16:12:48 GMT -6
Hi Fred
Actually the weapon advantage was to the Indians because you can apply Lanchester's theory to rate of fire as well as to absolute numbers of individual guns or even bows and arrows.
The cavalry advantage, which was in respect of range, was really only seriously attempted by Reno as far as we can tell because the terrain he initially fought upon allowed him to halt at range and try to dominate his enemy. Unfortunately his numbers were too few so he could not respond to the encirclement round his left flank.
Regards
Mike
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Post by Mike Powell on May 6, 2007 16:42:20 GMT -6
Mike,
[glow=red,2,300][/glow]Actually the weapon advantage was to the Indians because you can apply Lanchester's theory to rate of fire as well as to absolute numbers of individual guns or even bows and arrows.
Right on the head! A complimentary "I Hear The Music Of The Spheres"
pocket protector will be in the mail tomorrow.
Yours,
Mike Powell
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Post by mcaryf on May 7, 2007 3:51:29 GMT -6
I just want to try an idea on you and my apologies to the ex-military types if I use terminology in a non-standard way.
Is it possible to consider the progress of the battle in terms of the ability of each side to apply suppressive fire?
Thus the typical initial army tactic is to have its troopers out in the open, ideally standing or kneeling in skirmish lines or even mounted, able to keep the warriors heads down so that the troopers have a majority of alert people ready to fire as and when a warrior shows himself. This seems to me to have been the initial situation on Calhoun Hill. A lot of Indian testimony speaks of the troopers being very brave and this is because they are out in the open not seeking cover which the warriors interpret as a bravery display rather than a tactic.
Over time the cavalry position erodes due to casualties and as the warriors are able to produce flanking fire and encirclement so that their own men are less suppressed whilst the cavalry are more suppressed. Eventually we can track forward to the position on Custer Hill, here the cavalry are largely suppressed lying behind horses or flat on the ground so now it is the warriors who are able to move forward more freely, apply indirect fire and be ready to fire at known trooper positions when heads are raised and eventually charge forward.
In another post I did some simple arithmetic to indicate the volume of fire that the warriors might have been able to apply against Custer Hill. Actually the Lanchester rule breaks down at a certain stage because when the odds become too great the larger force just cannot bring all its superiority to bear (e.g. the 300 Spartans). This was in fact reported as the case at LBH by the Reno Hill survivors who indicated that there were not enough firing positions available for all the warriors. Even so the warriors would have been able to apply substantial suppressive fire but probably not in a well coordinated way. Thus the Reno Hill position would probably have fallen if the warriors had been organised enough to apply suppressive fire from one axis whilst preparing to charge from another.
I am sorry this has proved somewhat rambling but the point I was trying to get across was that Indian accounts can be read to track the changing ability of each side to apply suppressive fire. The troopers on Calhoun undoubtedly did this for a while and those coming over the battlefield reported piles of 20-30 cartidge cases at skirmish line intervals. It is interesting to consider how long this stage lasted. Reno's men seem to have fired off nearly double that quantity in about 15 - 20 minutes but Reno's men possibly thought they had better targets. Even so might it be that the smaller Calhoun cartridge totals also represent about 15 minutes of fighting?
RA Fox tends to write about demoralisation being the cause of less cases being found on Custer Hill but surely it is much more to do with suppressive fire and the greater difficulty in firing your weapon once suppressed. Demoralisation and suppression are to some extent related but I feel RA Fox overstates his case to make it more dramatic.
Regards
Mike
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Post by Dark Cloud on May 7, 2007 4:55:04 GMT -6
Dramatic and/or relevant. He can only make those assumptions and statements if the field were more virginal. But Fox was one of the first to apply this, and was trying to make larger points.
As I recall, there was one (1) source for the numbers of cartridges at Calhoun Hill: his brother-in-law Moylan. Everyone else seems to reference it rather than have actually seen these piles of shells themselves. It's not even like most positions there - itself a guess - featured such piles. Some. And, again, who fired them at what?
There is no Indian testimony, but of the accounts citing soldier bravery it's very important to note when said and by who.
Realizing how annoying this constant, nasal harp of mine is, I'd like to take advantage of this to - if not drown it outright in the tub - point out that it is not I formulating dancing angels. You guys start with these assumptions way outside any evidence locker and try to find solace in math, as if math covers up the utterly arbitrary assumptions that the math is based upon.
There are no angels to dance on pinheads or on the stripper pole. Never were.
More to the point, formulas designed to explain the Battle of Jutland and battle lines of dreadnoughts are questionable on land where movement is much more frequent and hard to forecast, but it is odd that the projected dead of the Indians by the formula corresponds rather on the nose with generally accepted Indian reports of their number killed.
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Post by AZ Ranger on May 7, 2007 7:48:35 GMT -6
RA Fox tends to write about demoralisation being the cause of less cases being found on Custer Hill but surely it is much more to do with suppressive fire and the greater difficulty in firing your weapon once suppressed. Demoralisation and suppression are to some extent related but I feel RA Fox overstates his case to make it more dramatic.
Mike I would think the most popular site would be picked over and cleaned by souvenir hunters. Some were probably removed the day of the burials. Who would not have wanted to have one of Custer's last fired cartridge case from LSH.
As I recall, there was one (1) source for the numbers of cartridges at Calhoun Hill: his brother-in-law Moylan. Everyone else seems to reference it rather than have actually seen these piles of shells themselves. It's not even like most positions there - itself a guess - featured such piles. Some. And, again, who fired them at what?
DC
I am not sure what they are describing in the first place. Is 10 - 15 cartridge cases scattered in a 8' diameter circle a pile? I don't think the single shot Springfield was capable on making a pile. There is to much movement of the operator between shots. If it is just scattered about a point then the Indian firing his new rifle could make the same placement of cases around a body.
AZ Ranger
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Post by Mike Powell on May 7, 2007 8:02:58 GMT -6
Mike,
I think your suggestion that this is a story about fire is well taken. The maneuver phase of the battle results in the natives establishing the boundaries. Custer achieves nothing with surprise and concentration. Once set, its a play board for the N-Squared Law, which only means it got much worse, much quicker for the losers than they would have imagined, given their background in linear equations.
DC,
If you haven't seen the angels get on the poles, you've been going home before midnight.
Yours,
Mike Powell
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Post by Banned on May 10, 2007 8:25:01 GMT -6
Custer achieved surprise -and he wanted to avoid the concentration of Indians by attacking them with Benteen and Reno from different locations.
It never happened. Benteen wasn't there and Reno ran away.
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alanw
Junior Member
Posts: 74
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Post by alanw on May 10, 2007 11:29:26 GMT -6
Hi,
I think I recall a documentary claiming that towards the end of the battle there were 700 rifles/guns trained on LSH. One body was found in recent times with cartridge shells from 13 different weapons in the vicinity.
Alan
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Post by Banned on May 10, 2007 11:50:21 GMT -6
Garry Owen !
Archaeological studies stated that only 150 modern weapons were used by the warriors, which is pretty low (and contradicts the theory of superior fire power). Indians had also a lot of pistols and short-range weapons (they loved to shoot while on horse), and also very old weapons. It could explain the cartridges.
Gosh, I love your picture near GAC's grave. I would have dreamed to do that.
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Post by conz on May 10, 2007 11:52:37 GMT -6
Gosh, I love your picture near GAC's grave. I would have dreamed to do that. Just an internment marker...not a grave. Custer and Libby are buried at West Point, you know. With a great, BIG, marker. <g> At least we think it is Custer...for Libby's sake, I hope so! Clair |
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Post by crzhrs on May 10, 2007 12:04:37 GMT -6
Indians with no superior firepower, no organization, were surprised, were killing each other . . . and they still beat Custer!
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Post by Banned on May 10, 2007 12:08:05 GMT -6
Just an internment marker...not a grave. Custer and Libby are buried at West Point, you know. With a great, BIG, marker. <g> At least we think it is Custer...for Libby's sake, I hope so! Clair Yes, I know, I visited West Point in 2000 and put a flag near Custer's grave. I called Custer's marker "grave" because it's where he actually died and was buried for a year. It's... spiritual ;D |
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Post by Banned on May 10, 2007 12:10:02 GMT -6
Indians with no superior firepower, no organization, were surprised, were killing each other . . . and they still beat Custer! Thanks for the support of Chief Reno ("White-Man-With-Rolling-Eyes") and Chief Benteen ("Slow-White-Man"). These two admirable Indian chiefs just gave Custer to the enemy. |
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