Terrain effects part 1: Elevation and slopeUsing the terrain has always been a crucial part of battle tactics. There is inaccessible terrain like rivers or steep slopes that can be used to protect the flanks of a battle line, there is elevated terrain that can be used to get both an overview of the battlefield and a well-defensible position, terrain may create chokepoints that can be exploited as in the battle of Thermopylae... The possibilities are many.In the following, we study a few of the effects elevation and reserve thoughts on terrain cover for the next section. Basically, the effects we want to study have to do both with elevation and slope - higher elevation grants a better line of sight as well as better range for projectile weapons, slope makes terrain more difficult to cross and aids the upper party in pushing back the lower enemy. Generally slope can be along the direction of motion (i.e. the unit actually moves up or down) or across (i.e. the unit moves on sloped terrain but keeps its original elevation).
Caloric effectsWhen a slope is along the direction of motion, a moving unit goes up or down. If the slope rises 5 meters for every 10 meters walked and the unit marches at 60 meters per minute, it means the whole mass of the soldiers and their weapons and gear needs to be lifted by 0.5 meters every second. That actually requires a power of nearly 400 W (*).How does this compare to 'just' walking? It's fairly comparable, a slow advance walking pace takes about 250 W. So walking up a slope makes walking harder and for a really steep slope it gets really hard (we kind of knew that, right?). But by combining exercise tables with the computation of how much weight needs to be lifted, we can compute how much harder walking uphill is. How, the standard reaction of a walker is not that he spends more energy to keep the same speed, rather he slows down and walks with the same energy consumption. So the caloric effect will tell how much an unit slows down when walking uphill and how much it accelerates when walking downhill (up to a point, because at some slope footing becomes difficult).
Angle of reposeWhen you pile materials such as sand or earth, the pile will only be stable up to a certain angle, the so-called Angle of Repose (for earth, it is between 30 and 45 degrees). Close to that angle the pile becomes slippery and prone to avalanches. In nature, rain will erode such surfaces heavily and the only way to stabilize them is to have rock outcroppings or a network of roots.What this means is that nearly inevitable, footing will be very difficult close to the angle of repose in the terrain - either because the ground is prone to avalanches, or because it is rocky or criss-crossed by roots or cut deeply by erosion. And that means that a military unit, especially in formation, can not properly march on it, much less fight. And that is true regardless of whether the slope is along or across the direction of motion. So even if the caloric effects says that going down a steep slope is easy, the footing may be so poor that it can't be done in practice. In the simulation, the angle of repose basically restricts how fast a unit may proceed across the slope at all.
Pushing and bracingIt should be obvious that pushing someone up a slope is harder than pushing down. This is first an effect of potential energy - which is required to lift something but released when lowering something. In essence this is a caloric effect.There is however a second effect. When we push an object, we have to transfer force into the ground. We do this by bracing one foot into the ground - the resulting friction force can then transfer a horizontal pushing force (this is why pushing an object across ice doesn't work very well - the friction force is too low - we can walk on ice because that requires vertical force, and the ice provides that by virtue of being solid, but we can not push because it provides no significant friction by virtue of being slippery). Now - when standing on a slope, the angle under which the foot touches the ground changes. Imagine a sheet of ice sloping 45 deg up behind your back - you could brace your foot perpendicular to the ice sheet, no friction force would be required at all. Generally we can brace into the ground better when we're facing downslope and worse when facing upslope. The precise factor is a function of the angle under which the foot is set, body mechanics and friction coefficients, but leaving pathological cases (ice) aside and assuming a 45 deg bracing angle on level ground, the slope corrections to pushing and bracing ability can be estimated by using trigonometry. In the simulation, this is done whenever a pushing power comparison is done, providing an avantage to the unit which faces downslope.
Line of sightWhen arraying infantry and archers on a plain, there's the issue that archers need to see their targets, and hence they can't be behind the infantry. They can of course shoot over an infantry unit, ballistics allows that, but accuracy is severely limited because they can't see the arrows land, the ranks in front of them block the view. This is no longer true when it is possible to position archers on a hill behind an infantry screen - the elevation difference now allows them to see the targets.Generally line-of-sight is complicated - it is not only influenced by the relative elevation of archer, target and units in between, but it really is sensitive to terrain details - a fold in the terrain can hide a target temporarily, a small wiggle in elevation can block the sight. In the simulation, line of sight is checked for every ranged attack when the option is selected, both on terrain and other units potentially between archer and target. Since this is computationally rather expensive, using the option severely slows down simulation speed.
BallisticsOn its trajectory, a projectile slows down as it climbs the ballistic arc and accelerates as it falls. When the arrow thus hits a target at the ballistic arctop, its kinetic energy is close to zero and it has no armor penetration power. Generally projectiles lose range and power when the target is on higher elevation than the archer and gain range and power when the target is standing lower. Positioning archers on high ground thus helps both with line of sight issues and makes them more powerful. The ballistic properties of a projectile along the trajectory can be calculated for any relative elevation between archer and target with relatively good accuracy when initial velocity and air drag is known, and tabulated forms of these computations are used in the simulation to adjust range and projectile power.(*) I realize fully well that fitness sites usually give energy consumption in calories per half hour and other difficult to compare units - as a physicist, I prefer to use SI units everywhere so that you can see a direct relationship between energy release from weapons, energy expended when marching and so on. Bear with me, it'll pay off. Back to main index Back to science Back to historical battle simulation Created by Thorsten Renk 2023 - see the disclaimer, privacy statement and contact information. |