Lessons from Geometrics

Lessons learned from using Sprocket's geometric alpha v0.2.4 and on

Introduction

Lessons on Geometrics in Sprocket
by Brygun


Sprocket is a tank design game which as of 0.2 has visual internals, geometrics, rather than simply assigning cubic meters of volume. You now place ammo racks into notches of sponsoons and do “human tetris” with the crew. It may take switching into the beta and voluntary alpha versions of game.

Having worked up a few vehicles there are observations on how the geometrics affect designs. The discussions will cover how things like engine size impact the tank. This isn’t going to cover individual key strokes.

In many cases the reference is to the influence of a factor like how the number of cylinders influences the length of an engine. An inverse influence means as something gets bigger its affected matter gets smaller and vice versa.

Terminology is being written assuming a familiarity with basics and may be challenging for those new to tank designing. If there is a matter difficult to understand try editing a tank to see the described affect.

Hull lessons:

Hull lessons:

Hull height:
The minimum hull height will be set be one of the following:
- Height of the engine which in turn is based on the size of each cylinder, # L.
- Height of the driver or other persons in the hull. Changing posture such as having the driver leaning can change this
- Length of ammunition if carried vertically

Additional hull height needs will go up from the drive shaft(s) should you have the engine on one end and the transmission on another.

Hull width:
The minimum hull width is most strongly influenced by the size of the turret ring.

Hull rail transport width:
The maximum width can be limited by considerations for transporting by railways. While this isn’t mandatory it is something the real tanks dealt with. Different nations have different standards with Japan having comparatively narrow railways which led to their early tanks being rather small.
For Canada I found references for the width that rail cargo can be for safe passing normal rails to be eleven feet. This means that if there is double track with trains going each way the cargo can be that wide without issue. Anything wider requires limiting rail traffic and may be a problem on what turns, narrows or tunnels can be passed.
Railway flat cars come in different sizes with different widths. The narrowest that came up in the Canada reference was 9 ft 6 inches. This makes this the maximum the inner part of tracks can be. In fact a good chunk of the track should be within that. This though was a narrow flat car with most flat cars being a little wider.

Engine size

Engine length comes from the number of cylinders x the size of cylinders

Height and width of the engine are based on the size of each cylinder.

Max safe rpm is inversely affected by the size of cylinder.

Torque is influenced by the size of cylinder and the number of cylinders.

Max power will be a few hundred rpm below the engine max rpm. Max rpm is influenced by the number of cylinders and the size of each cylinder.

It is good to set the allowed rpm to be at least 100 rpm below the max rpm if not 200. This can happen when the tank is speeding downhill.

The downshift should be set at a 100 step below the ratio of your transmission gears x up shift rpm. This means when going down from the high gear there will be a valid 100 rpm step for the lower gear to operate from. For example if your transmission ratio is x0.55 and your up shift rpm is 3,100 the result is 1,705 making a suitable downshift as 1,700 or 1,600. As the 1,705 and 1,700 are very close you may avoid gear hopping by using the slightly lower 1,600.

Remember the actual speed and acceleration of tank are based on not just the engine but by the transmission gearing and size of the sprocket of the tracks.

Idle is manual set with the default being 800 rpm. Higher rpm may help when on steep slopes where you stop and start though the benefit is only a fraction of a second before the engine adjusts to the current rpm. In theory a lower rpm reduces fuel loss when stationary but that is noticed in the battle times of sprocket.

Transmission

Pivoting at zero speed has the influenced by the size of the G1 forward and G1 reverse. A decent turn rate may be found by increasing them both until while pivoting the engine reaches the 800 rpm idle speed. If the engine is below this it is struggling to spin the tank. Using this my G1 which were 5 are now often 7 or higher.

The diameter of the transmission cylinders is set by the size of the largest gear, likely G1.

The length of the transmission cylinders is set by the total number of gears, both forward and reverse. As of this writing we don’t yet have the option to add a single master reversing gear. That is for one more gear you access all the same gears as for going backwards as forward.

Each gear adds weight based on its size. Thus adding more smaller gears has only a very small affect on overall tank weight.

The more gears you have the smoother turning you may have and more adaptable the tank is different conditions such as different slopes or moving diagonally along a hill.

Historic early and mid war tanks might only have 3 to 5 forward gears and only one reverse.

My own tests favor 5-6 forward gears and 3-5 reverse gears. The first gear (G1) will be used to get the tank started and deal with steep slopes. The second gear is used once moving and so on. The extra forward gears are there to have a higher top speed, more acceleration to the speed and better forward climbing performance. Reversing is not done as much but is important in the battles to dash down and back up hills for “pop up” attacks, speeding backwards when being charged in closed quarters to keep the better forward armor to the enemy while bringing the gun around and being able to climb slopes backward if you got stuck, such as in a shell hole.

An extra forward gear is useful for overdrive. Modern cars with this once at a road speed can switch to over drive. This smaller ratio in the higher gear makes acceleration worse but it allows a lower engine rpm to maintain the speed. A use for this is during long range highway driving. For tanks this would be more fuel efficient on operational not tactical redeployments.

My own preference is to match the reverse gears in one of a few ways to the forward gears. This keeps a handling performance whether driving forward or back. One such pattern is the odd number approach. In the odd number assume 5 gears forward (ignoring overdrive) then the reverse can be 3 gears. Reverse 1 = Forward 1, R2 = F 3 and R3 = F 5. The ratios for shifting will be off and steering slightly less smooth but you get a similar reverse climb when stuck and a decent speed for escaping an oncoming enemy. This would take a length of geometric transmission based on 8 gears or 9 with forward overdrive.

The next steps will be a bit of math.

The spread of the gears is the ratio between G1 and your highest gear. Exampe: G1 is 7 and highest is 0.7 then the spread is 7 divided by 0.7 equals 10.

It uses n-root. For example 2-root is the common square root such as 3 is the 2-root of 9. A scientific calculator app on a phone or computer will be useful. The # of n is the number of steps in gearing. This is the number of gears minus one. So for 6 forward gears it is the 5-root that is needed. For our example we need the 5-root of 10 which is 1.59.

The gear ratio is 1 divided by the n-root. For our example that is 1 divided by 1.59 which is 0.63

Each gear is then found by multiplying the lower gear by the gear ratio. For the example G1 of 7 x 0.63 makes G2 as 4.42.

Example of gearing:
# Forward: 6 (5 + over drive); #Reverse: 3; Total # gears: 9
First Gear found by rotation test: 7
Overdrive gear found by speed test: 0.7
Gear spread = 10, n for n root = 5, n-root = 1.59, Gear ratio = 0.63;
Engine: up shift found by safety limits 3100; downshift: 2000
F1 7
F2 4.42
F3 2.78
F4 1.76
F5 1.11
F6 0.7

Rear gears using odd gears
R1 7
R2 2.78 (same as F3)
R3 1.11 (same as F5)

Shaft layouts

In geometrics you will need to place the transmission(s) somewhere. With the gear number and sizes you will have the diameter and length of the transmission. As of version 0.2.5 you will have two cylinders, one for each track.

Selecting the tracks you can set them to either have a forward or reverse sprocket. There are spheres with only the pipe in that need the sphere to end near the chosen end. The pipes are the drive shaft(s). You can split a shaft to have new lengths to allow redirection paths. Each shaft joint gets a sphere. Selecting the sphere give the choice to remove the sphere and turn the two shafts into one.

To describe the shape of shaft layouts letters will be used. Each can go to forward or rear sprockets. The engine may be turned so that the initial drive shaft is coming out the front or rear of the engine. Usually this will be same side as the sprockets. Each will have pros and ♥♥♥♥ that will be reviewed.

Maintenance will be discussed as if these were real though this doesn’t affect Sprocket battles. Maintenance would be more routine tasks like fluid checking and changing. Swapping refers to fully removing the transmissions, such as if battle damaged, and putting a new one in. If not mentioned it likely is the same as maintenance.

The simplest is T which has one shaft from the engine which goes inline with the sprockets then a short branch, with the transmission cylinders, to the sprockets. This has very limited length for transmissions as it is less than half the width. Perhaps 3 forward and 1 reverse gear might be present. It reflects many World War 2 transmission setups. Maintenance is done by removing it through the forward or aft armor, such as on the USA M3 and M4 tanks.

Y comes out of the engine then splits in two going at an angle toward the sprockets. Typically the driver would sit in the middle of the Y arms. There is enough length for a good number of gears. Maintenance for routine tasks is done by direct access interior but swapping is very difficult perhaps by wrestling the heavy transmission up through a turret hatch.

U comes out of the engine the splits going directly to the sides of the vehicle then shafts and transmission run along the sides to the sprockets. This gives a lot of length for many gears. Maintenance can be decent though interior shelves or gear may have been temporarily placed around the transmission. Removal would likely be through two small hatches in the end armor. Another quirk of U is that it can on the side of the turret basket allowing a deeper turret but in turn lower part of the basket can’t be as wide.

Reverse U has the engine with the drive shaft first coming out of the front. Then splits into two shafts go to the side then the next shafts run along the sides of the engine thus reversing the direction. It is on the shafts going along the sides of the engine the transmissions go. This gives good room for gears while avoiding issues with a turret basket. However this area is often where fuel tanks could go so fuel quantity may be lower.

Z comes out of the engine going a long way down the center. Then it splits in two going close to each side. Each side comes up a different height and angle so each transmission can fit in sideways. Mirroring needs to be turned off. It gives room for a good number of gears being most of the width. It is however complicated due to the parallel near each other of the transmissions. Maintenance would be awkward and removal would be through the end armor.

Example of a forward Z transmission
https://steamcommunity.com/sharedfiles/filedetails/?id=3259709340

Firepower

For now shells are 3 calibers in length meaning the length is 3 times the diameter. Thus as 75 mm shell is 225 m long.

Cartridge length is the sum of shell length plus the length of propellant, thus 3 x diameter plus propellant.

For a giving length of barrel the penetration depends the most on cartridge length. Trading 5 mm of diameter inversely with 15 mm of propellant will result in very close to the same penetration.

The explosive power of the shell is based around the diameter of the shell.

The mass of a shell is based on the diameter of the shell, since that also sets its length. The mass of propellant is based on shell diameter x propellant length. Typically the combined cartridge mass is mostly shell not propellant.

To fit a longer cartridge, thus higher penetration, in a turret vehicle the turret ring will need to be larger. In turn this will mean a wider tank. Some length can be gained by having the front of the turret project forward. As of this writing we do not need to account for turret balance.

Barrel length will affect the penetration. Longer barrels make the penetration go up. The expansion ratio goes up as barrels get longer which is how many times the gases, former the propellant solids, push along. As the barrel is external it can be sized to other considerations.
A short barrel adds less weight, less pen, less accuracy though still fine for explosive rounds or those for limited protected targets. A medium barrel can be considered as one that comes close or to the edge of the front of the tank. This would be useful in shipping with better penetration than short. Long barrels, L40 – L50 (40 to 50 times the shell diameter) will get expansion rations of 6 or higher giving the highest penetration. These long barrels protrude beyond past the front of vehicle. In real world situations this can also lead to “piking” when the vehicle is going downhill the barrel gets stuck into the ground.

Bonus: Concepts

As with any open design game it is important to have a concept for the vehicle. This may be as simple as “my first tank” just to see how things come together. Concepts will affect things like size, weight, and type of weapon(s). Often with concepts may be weight limits such as the well known 30 ton lifting cranes on the Liberty ships and in harbors setting the 30 ton weight of the Sherman.

The classic triangle of armored warfare has three factors: Firepower, armor and mobility. To that consider how many vehicles are present, this will be elaborated on shortly.

Firepower is mostly about the type of main gun and some nations, like the USA, also liked to have multiple machine guns. Ammunition load is also a part of firepower.

Armor is the vehicles defense ability making up much of the weight of the vehicle. External choices involve angling, curves, sponsoons, skirts on the sides or external space armor. Internal choices may include crew shields, bulkheads and internal layers of armor. As of this writing its not certain if internal armor will affect combat in the game. Hopefully it will one day.

Mobility is about the vehicles moving, its ability to climb, rate of turn and speeds. Also is this area is the vehicles fuel supply. The range of vehicles in Sprocket isn’t obvious with an alternate basic rating to compare the fuel per ton to historic counterparts. An over dive gear can increase range on roads.


My own views add a fourth which is the “availability” or “presence”. The starting letter “P” being a different letter than “A” which could in some situations be confused with armor. This factor comes down to how many vehicles are present at the time of action. This encourages smaller vehicles for more balanced designs. It also includes factors like the ability to do maintenance, be shipped over seas, cross bridges, use temporary bailey bridges and use railways.


Concepts are very much influenced by a nation’s idea such as the term “cruiser tank” was used by the British but not by other nations.

Possible concepts from various nations include:

= Self propelled gun
A way to move a gun on a hull, no turret, across a battlefield such as the early Stug with the larger diameter shorter barrel.

= Infantry tank
A slow moving turret tank meant to provide direct support infantry where it needs good armor for the hits it will take such as the Churchill.

= Cruiser tank
A good speed turret tank with a gun emphasis on armor piercing and thus medium armor. An example being the Cromwell.

= Support tank
A medium speed tank with a gun for providing larger shells, 75 mm and up, for a good high explosive affect such as the early Panzer IV and the KV-2.

= Breakthrough tank
Meant to punch a hole through enemy lines then continue on beyond to attack more vulnerable enemy assets.

= Light
A term refering to the weight, which varies by era, though should also mean a greater mobility with less armor and usually lighter firepower, such as the Stuart.

= Medium tank
Another term refering to weight that would represents large production runs with good qualities in all design aspects such as the Panzer III (in the early war), Sherman and T34.

= Heavy tank
Another term based on weight with an increased of armor which will also reduce the mobility. Firepower might be heavier though in many cases was similar to the medium tanks.

= Tank destroyer
Meant to fight other tanks with less features. In the USA these were turreted with large reduction in the armor, such as no turret roof, to have a mobility so as to move to where enemy tanks were attacking such as the Hellcat. The German tank hunters had an increase in protection and firepower by not having a turret such as the Hetzer or later long gun Stug. These tended to work from defensive or ambush positions where enemy movements might be predicted.

= Self propelled artillery
Simliar to the self propelled gun in this case to have a high angle of fire for longer ranges and to use plunging fire. Armor is reduced and may exclude roof armor. Mobility is still good leaving capacity for an increase in firepower to very large guns such as 105mm and 150mm. These shells doing their work by explosive power rather than straight in armor penetration. An example being the Hummel.

= Anti-aircraft
Variants of armored vehicles were made in various ways to have weapons for fighting aircraft. Often these had multiple weapons to get a high rate of fire to get hits on fast moving aircraft. An example being the Ostwind.

= Cavalry
One term the author likes to use based on looking on taking on the multiple roles of the horse cavalry. This includes scouting, flank protection, mobile response, breakthrough and exploitation of breaks in the enemy line. Similar to the break through and cruiser concepts the cavalry tank are to have a good mobility with good range to move on both the operational and tactical level. Armor and firepower abilities will be influenced by whether working using a light or medium weight class.

= Mobile artillery position
This is another author term that expands on the self propelled artillery to have a better ability for self defense with machine guns and possibly a light secondary cannon. There would be consideration, space and crew, for the communication and planning of long range indirect fire. It is enclosed for better protection from incoming enemy artillery fire. With good firepower and good defense they design balance has less mobility and/or larger vehicles.

[Sweetwater]

If you want higher gears for pivoting better, just increase the climbing angle in the calculator to get the same result.
As for the overdrive gear, most scenarios in Sprocket have terrain that's too bumpy and rough to warrant any practical use of an overdrive gear. As it is, the calculator usually gives a top speed that requires an unusually high amount of travel in the flat sandbox to achieve.

[Brygun]

@Sweetwater its a decent one. However it doesn't (currently) do the pivot vs rpm test. You may want higher gears for that or other reasons. Not sure how or if it handles the "overdrive" gear concept

[Sweetwater]

Could just use https://sprockettools.github.io/TopGearCalculator.html to deal with the transmission math. Otherwise, nice guide!