"Slope and movement" Topic

I am (still) working on our computer wargame set in the age of gunpowder.
At the moment I'm "doing" movement costing.

I have elevation per pixel so I can calculate slope per pixel a unit is to cross.
Or not cross, if the slope is too great.

What I am need is to cost that travel and to stop invalid moves.
At it's simplest, there should obviously be no trotting up or down 30 metre cliffs on neddy.
There will be a maximum slope different troop types and formations ought to be able to cross.
Travel up and down slope should take longer.
There's a formula for runners which I found but this is one person in shorts and vest.
Just adding the elevation change in metres to distance travelled can't be "right".
I know from experience fell walking that the water bottle you barely notice carrying on the flat is pretty soon a giant lead weight as you head up a mountain.
Infantry with like 60… 80 pounds of kit in woollen uniforms are going to notice elevation change way more than runners.
I would think.

I've also looked at one or two kriegsspiel-esque rule sets for their ideas.
Cannon are stopped by what I found surprisingly low grades in them.

I was wondering what research/ideas people have on this.
I would have thought the modern military must have some way of estimating this for infantry.

I think your key word there is "estimating".
I also think there are far too many variables involved to get truly accurate numbers on this (humidity, temperature, wind speed and direction, type of ground, amount and type of ground cover, hydration and fatigue levels of the troops, etc, etc, etc).
I also think that whatever you come up with, somebody is going to disagree.
If you have data on modern runners in shorts and sneakers, I would use 1/4 to 1/6 of that speed.

Good luck!

I'd think that using the percentage of the slope (45degree=100%)/2 as a cost in Movement rate would work. But you need to know what the slope is averaged across the frontage of the unit.

Basically taking stairs is half movement. while that long slope will wear over time.

I think that Saber6 has it.
Slope times X, where X is a factor of who is going up; i.e. Skirmishers, Formed Line, Horse (Light or Heavy), Artillery (Foot or Horse), Couriers (Runners or mounted) &c. Obviously at a certain point the speed will equal Zero. Or may be increased by extra pullers if your rules have scale time to organize that.
Then do it all again downhill.
And then cross hill. :)

For armored vehicles I did a gross approximation, which I found useful though not accurate. If you take the output power of a tank and assume it is 100% efficient you can work out the vertical velocity at which all the engine power is absorbed by the increase in potential energy.

From that speed and given an angle of assent you can work out what ground speed (allong the hill) at that gradient is required to achieve the vertical limiting speed. Why is this interesting, it showed that at even modest gradients (1:10)the ground speed is low just because of the vertical assent.

Now a good cyclist well fed can achiever an output of 145W max continuous for a bit. A soldier with little training or poorly fed be less. Therefore given his weigh plus pack you can at least calculate limits in a similar way.

The same could be said for horse drawn vehicles. One horse power is probably not a bad estimate for a less than ideal horse. You can approximate its weight and the weight of the cannon and I suspect even the THEORETICAL speed is far lower than you would have thought even again on modest gradients.

These theoretical figures at least give you a credible rank ordering of ground speed and gradient although the figures will be over optimistic.

The mountaineering navigation rules might help, have a search for Naismith's Rule. It roughly allows you to work out timings to travel a route. Several variants, my preferred version (i.e. the simple one) is normal walking speed = 12 minutes to cover 1km. Add 12 mins for every 100 metres of ascent and descent. Simple, about right. The descent bit is important, and oft overlooked.

there are a number of 19th Century military wargames starting with Kriegspiel that calculated by Military men in both in minutes and slope angles. Totten's was the most specific.

Thanks for the ideas.

The method has to produce reasonably believable numbers.
As someone mentioned, whatever I do there will be someone doesn't like it.
It has to be practical.
We have no mountain climbing battles planned.
The big rock at Isandlwana will be there in that game but I don't expect anyone to fight across it.

Basing it on a Totten's Strategos seems like a good plan.

The rate of slow down probably shouldn't be a straight line or an abrupt stop and it should be related to elevation change.
An exponential scale of cost up to the max seems about right.

I first considered tenths, but that seems to give way too much effect.
Maybe fifths.

If we take infantry with a max slope of 20 degrees.
Divide by 5 = 4 deg steps.
Up to 1 step is 4 deg or less and adds 1 * elevation change.
5 to 8 deg adds 4 * elevation change.
9 to 12 deg adds 9 * elevation change.
13 to 16 deg adds 16 * elevation change.
17 to 20 deg adds 25 * elevation change.

And pre convert degrees to gradient to reduce the cost of each px calculation.

I'll plug those numbers in and see what happens.

I think one of my sentences couod be read as dismissing some advice.
That was not my intention.
I'm grateful for everyone's time.

I took a look at naismith. It's a good estimate for what it's aimed at.
I need something produces reasonable results at the tactical level. For formed units loaded with backpacks and whatnot.
Over relatively low elevation changes.
My quick checks indicate naismith would not produce enough slowing.

But Naismith is real! Are you saying you want unreal answers. Mountain walkers tend to have heavy backpacks so it looks very sensible.

Then look at the effective unit speed / formation. If overall they stop often to dress line, they would effectively catch their breath at the same time. So… it depends. I am not sure these stops are into Kriegspiel or left to the feelings of the umpires.

Can't think of much worse than negotiating hills with a brigade of close-order troops.

Open-order screens possibly.

Troops in file could go across a slope.

I'd want to either be going straight-up or straight-down in small columns.

Would need a lot of coordination – lots to go wrong.

Gentle undulations are what's required – look over there! there's a heath/moor!

I was a member of a UK mountain rescue team for 15 or so years. On a call out we would individually have to carry 20-30kg of kit. Naismith is pretty accurate with that sort of kit. We were reasonably fit, used to traversing the terrain on our 'pitch', and most walkers would say we walked quickly – a less experienced/fit walker with the same weight of kit would have been slower.

Don't forget that the add 12 mins for every 100 metres of ascent/descent is in addition to distance travelled. A 100m rise over 1km (1 in 10 slope) would take 24 mins. A 50m rise over the same distance (1 in 20) would take 18 minutes.

Trying to keep a line search formation up a slope is difficult (regardless of how steep or gently undulating it is), and to keep the line intact slows you down considerably (even with lots of practice).

Naismith is a good, reliable and reasonably accurate, simple navigation timing rule. I have used it throughout the UK in a wide range of terrain, and it works reasonably well regardless of what is under foot: flat farmland, the Downs of Southern England, the Peak District moorland, and the more archetypal mountains of Wales, the Lakes and Scotland.

There's a reason that Naismith is taught on mountaineering/walking instructor courses.

20-30 kg is way more than we used to carry rambling.

I'm reminded of fell runners.
They used to run past us with a breezy "good afternoon".
As we wheezed and struggled.
Oh, how we loved that.

Maybe a super fit mountain rescue team would race past napoleonic line infantry similarly.

And then there is unit size and all that line and file stuff.

My understanding is that a unit attacking up slope would pause more frequently to dress lines ( as jcfrog suggests ). Also to rest a bit. Even if under fire, commanders wanted their men capable of fighting when they eventually contacted the enemy.

It would all depend on the slope grade, and troops could dress while moving, so….

For example, Soult's two divisions in battle array marched up the Pratzen Heights in what Soult estimated was 20 minutes…and that was a distance of about 1600 yards. That is 80 yards a minute or French 'quicktime.'

Of course, I don't know what grade the mile of slope was.

Factors to consider for influencing movement up or down slopes, include condition of the ground. A bald slope is easier to cross than a slope containing vegetation. The more dense the bushes, the more difficult it is.
A sand slope may be difficult to cross as well. The Army has four classifications for desert terrain.
Another issue would be rain or past rain which would leave slopes muddy and impossible to cross.

That Pratzen heights 20 minutes thing.
Heights definitely suggests a significant grade.

A real world test.
Great stuff.

We could plug that into reality and see what the grade looks like.
Or I can anyhow.
I can import google maps elevation data and build an elevation map.

I just need to know where they started and ended.

I grabbed the data for roughly the right Austerlitz area, which gives me this:

You're seeing a hypsometric representation with a bit of false shading overlaid to emphasise slope.

You can see lat long for the map's corners.

Depending Soult's guys start and finish, a move kind of up the centre to the top of that ridge might be 30 metres elevation change.
The entire map varies between 184 and 385 metres.

Depending on the exact route, they would be in dead ground initially because it's steeper initially.

I've read that Soult estimate a couple of times.
Always wondered how literal that 20 minutes was.

I design and build software systems.
Being literal minded and questioning everything is a way of life.
A lot of people aren't quite so literal minded though.

I say to the missus…. "I'll be back in 20 minutes" then we talks to someone else later.
She says "Yes it took my Andy exactly 20 minutes to get back with my present. He's great."
( You can tell I'm making this up from that last sentence there ).

She might have timed it, she might not.
She might say that even though she knows it took me way longer. Maybe it took 40 minutes but if she says 20 she thinks she looks better because I rushed back just for her.

And memory is unreliable.
Particularly under stress.
I once interviewed 3 soldiers had been in the same ww2 battle.
They described 3 totally utterly different versions of events. You would think they were in 3 different battles rather than in the same battle, same unit.

Depending Soult's guys start and finish, a move kind of up the centre to the top of that ridge might be 30 metres elevation change.
The entire map varies between 184 and 385 metres.

The entire corps began behind the Goldbach and reached the line between the village Blaziowitz and Pratze, about 2 km in about 20 minutes, Soult's estimate. The Corps kicked off about 9:45.

Napoleon called Soult the "greatest Tactican in Europe." While I agree that the distance and timing edges around Soult's claim and observers' comments is fuzzy, his reported estimate fits the narrative. Soldiers in the field didn't have the same time estimation demands general officers did, particularly during the Napoleonic wars.

The way to get around that fuzziness is to find a wide variety of instances. For instance, the Allied columns were given times to engage in the Allied plan at Austerlitz. It is interesting to note that the Allies, moving into place in the dark traveled in column at about 60 yards a minute [All of them except one, which had problems with mud and a track that had to be cleared by engineers, so they averaged 40 yards a minute. That was over slopes… In the early morning light, Soult's divisions in battle formation made it at 75-80 yards per minute. In a wargame with 20 minute turns and 100 yards per inch, that is 16 inches upslope.

Yes, collect many instances and drop the extremes should give a better mean.
Another couple of years delay in delivery might get people excited though.

Interesting that the low end in extreme conditions is half. With a quarter reduction more likely.

I think Blazowitz would now be Blažovice and Pratz Prace.
They're in the valley and well below the ridge.
It seems the Goldbach would be the Říčka stream.

link

The stream is roughly 220m and the line across roughly 250m elevation.
Which is 30m over 2km.

If you look at the map there's a Y valley over towards top left.
This is where Ponětovice is now and the Říčka is the left branch and tail of the Y.

If they started from where Šlapanice is now then they'd first climb over a 20m higher ridge, down the other side and then up the slight rise. I guess no dam back then.
If they started below Ponětovice then it's ~30 metre gain in elevation.