Lanchester's Laws: The Maths of War
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- เผยแพร่เมื่อ 20 ก.ย. 2024
- Lanchester's Laws can be used to calculate the relative strength of opposing military forces to predict which side will win in a battle. Featuring Tom Rocks Maths intern Dan Hunt.
Lanchester's Linear Law (part 1) looks at the situation when combat takes place with a fixed front line - for example with troops advancing through a valley. This is perhaps most relevant to historic battles between infantry.
Lanchester's Square Law (part 2) develops the model further to include the situation where all soldiers are able to fight at once. This was developed by Frederick Lanchester during World War 1 where ranged rifle combat became the norm, but can just as easily be applied to archers as shown in the video.
Produced by Dan Hunt with assistance from Dr Tom Crawford at the University of Oxford.
Dan is a second year undergraduate student at the University of Oxford studying Physics and Philosophy. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: www.seh.ox.ac....
For more maths content check out Tom's website tomrocksmaths....
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beautifulequat...
I'm sure you'll all agree that Dan really nailed this one! Check out the other videos produced by TRM interns on the 'Mathstars' playlist here: th-cam.com/video/jceythNWBWE/w-d-xo.html
Your voice sounds broken!!!!
I used to have a copy of the US Army modelling equations, and, when I ran simulations of known guerrilla actions, and it quickly became clear why they lost so badly in Vietnam and elsewhere, as local knowledge, popular support and, crucially, surprise can each make between 2-3 times difference.
Absolutely. Insurgence type warfare is very very different to the traditional 'battle'.
The U.S won every major tactical engagement in Vietnam. They lost because the enemy because the enemy never gave up and the war became too costly.
@@ddddd9665 I guess the Tet Offensive doesn't count as a "major tactical engagement" then
Bro Vietnamese they dug underground didn't they?
Really enjoyed this one and the choice of background music for the desert battle was very nice as well :D
glad you enjoyed it :)
As an amateur mathematician (B.S.) and an Army officer, these kinds of models won't really be effective at a small tactical level such as in the examples because of time for planning and all the reasons you mentioned. However, on a large scale STRATEGIC level I can definitely see them being useful for the Generals planning entire campaigns. Especially if they managed to replace some or all of the assumptions with empirically demonstrated facts.
Edit: side note: the tactical rule of thumb is to not engage unless necessary if we do not have 3:1 strength.
Ive been watching a lot of Starcraft II videos and this just makes me want to figure out exactly how effective armies are against eachother on paper because there is SO much data available on each unit to refine this more.
Lanchester is so underrated!!!!
He's made some lovely sketches of vortex filaments behind finite wing
The lifting line theory should really be called Prandtl Lanchester theory
Anyway I'm rambling
Love from India!
Awesome - I didn't know this, I'll check it out :)
Aghh !! if only Leonidas did his maths homework...
😆
In fact Leonidas did the best math work here. By making combat on the narrow pass of the Thermopylae he effectively switched the combat scenario from a square one to a linear one, and thus the number of enemies was not so important as before. He was defeated but they did an inmense amount of damage to the Persian army. Persia won because they pushed numbers to a crazy amount, but lots of lives were lost compared to the wins.
R.I.P. General Reddington, and congratulations to General Blueington.
I second your sentiments, although I believe it was General Blueford?
Nice! Reminds me of War and Peace, 3rd section of Book IV, chapter II, where Tolstoi goes on a about Newton's second law applied to the force of an army, and the often crucial variable of morale (among other concepts spread across the book).
You see good application of this in wargarmes like Starcraft II. Phoenix battles especially, Even with the best engagement, having 8 units versus 9 units is a completely one-sided battle and ends with one person having 7 units to 0 remaining if you engage.
this is now my favorite video!
The definition of "effectiveness" seems to imply that it is quite random who wins, but the chances still grow proportional to the effectiveness. That would be the case for example if both sides shoot with arches and each side has a certain chance to hit the goal.
In most real world sports being only slightly better in what you do would make you almost always win a one-on-one. For example if your arms are slightly stronger than your opponent's arms, you would always win in arm wrestling against him. In that case the 20% stronger guys could be outnumbered 10 to 1 and still would eliminate all of their opponents.
So it makes sense for one side to find a way to be just a little stronger. For example if your arches fly further than the other's arches, there is a distance from which you can attack them, but they can't fight back. That would make you win against every number of opponents unless they can run faster than you or you run out of arches.
very cool video! nice
Great video!!!
Glad you liked it!
I guess some stuff like an artillary weapon might need four specially trained people to operate and if they are alive their effectiveness at killing the other army is really high but if one of them dies their effectiveness drops to zero. Or maybe if the other army gets too close.
This is a really great video! I make math videos using the video game Minecraft and this video inspired an idea for a video I can make. Thank you so much! Great job Tom and Dan!
Awesome - send me the link when you do :)
@@TomRocksMaths will do!
Who cares about real life complexities. I'll use this to dominate RTS games xD
Thanks for the video.
Is there a method to calculate the battle's duration using the Lanchester's model?
The force is relatively strong in this one? DDEEERN.
It reminds me of "the smaller force is a greater force's spoils" 48 laws of power
It is say that every Napoleon general was a able mathematician.
Dr Wesel Couch sent me.
Welcome :)
F for Reddington. xDDD
in the end the reds always win 🇨🇳🇻🇳