[UPDATED] Fixes to incorrect torsion bar suspension

[A1ex-Andro]

1). In the game, the suspension "torque" changes when the length of the swing arms is changed. It's not supposed to. Making the swing arms longer (increasing the "suspension scale") is supposed to increase only the "specific weight" parameter, because you make the weight of tank act at a larger distance away from the centre of the swing arm's rotation.

The "specific weight" parameter in-game refers to the torque acting on each axle due to the tank's weight. This is equal to mglcos(θ)/N, where m is the sprung mass of the tank (does not include the mass of the tracks, roadwheels, swing arms, etc.), g=9.80665, l is the swing arm length, θ is the swing arm angle from the horizontal, and N is the number of axles, all in SI units.

The "torque" parameter should change only if the characteristics of the torsion bar are changed. Here, I think you have confused torque with force. Increasing the length of the swing arm will decrease the downward force applied by the arm, which is equal to T/[lcos(θ)], where T is the torsion bar torque, l is the swing arm length, and θ is swing arm angle from the horizontal. Not the torque. To set the "specific weight" and "torque" equal, you need to think of both in terms of torque or both in terms of vertical force. One is a force acting at a distance l away from a centre of rotation, causing a torque about that centre of rotation. The other is a torque acting about a centre of rotation, which applies a force at a distance l away. In summary, the torque due to the specific weight changes with arm length (increases linearly). The torque of the torsion bar does not.

2). Specifying the swing arm length with an arbitrary "suspension scale" does not make sense. Replace it with a "swing arm length" parameter, specified in millimetres. In case you don't know what size the suspension is in-game, I used g=9.80665 and simple physics to determine that a scale of 1.00 corresponds to a swing arm length of 656.54331 mm (not even a round number!).

3). The torque of a torsion bar should increase linearly with the twist angle (how far the bar is twisted from the position that it would return to if the load was removed). This torque is given by T = kα, where k is the spring rate in Nm/rad, and α is the twist angle in radians. The spring rate is k = πGd^4/(32L), where G=78, d is the torsion bar diameter in millimetres, and L is the torsion bar length also in millimetres. If necessary, you can multiply the spring rate by π/180 to convert it from Nm/rad to Nm/°.

Here are the parameters the user should specify:

• Swing arm length in millimetres
• Torsion bar length in millimetres
• Torsion bar diameter in millimetres
• Torsion bar twist angle at 0° or "preset angle" (Think of it as the angle, β, that the swing arm would make with the horizontal if all load was removed from the torsion bar and it was to return to its untwisted position. This would also be the rebound angle).
• Bump stop angle (the maximum angle above the horizontal that the swing arm can reach before hitting the bump stop. This both limits the vertical wheel travel and the maximum shear stress that the torsion bar can be subjected to). There is a maximum limit for the bump stop angle to not allow the torsion bar to deform and fail. The game should not allow the bump stop angle to be set above this value. The equation is in the 2nd comment below this post.

Here is the resulting parameters that the game should display:

• Spring rate in Nm/° (k = πGd^4/(32L) in Nm/rad, where G=78, multiply k by π/180 to convert it to Nm/°).
• Rest angle (the angle θ of the swing arms when the tank is just sitting there on the design platform). Naturally, the swing arms on the tank model should already be at this angle when the user is in designer mode, so that they will stay that way once the user hits "play").
• Positive vertical travel or "bump travel" or "bump stroke", in millimetres (the vertical distance travelled by a roadwheel from the static position (rest angle θ) to the bump stop). More details in the 2nd comment below this post.
• Rebound travel or "rebound stroke", in millimetres (the vertical distance travelled by a roadwheel from the static position (rest angle) to the rebound angle β). More details in the 2nd comment below this post.

The rest angle, instead of being specified by the user, will now be the result of the specified parameters and should be calculated automatically, displayed to the user to one-tenth of a degree, and reflected in the tank model on the design platform.

• The rest angle is simply the angle at which the torque of the torsion bars equals the torque due the tank's weight.
• k(β + θ) = mglcos(θ)/N
• Then solve for θ:
• θ = mglcos(θ)/(kN) - β
• Note 1: the rest angle θ is a function of itself so it will need to be solved for iteratively.
• Note 2: the swing arm length l is in metres here, so remember divide l by 1000 if in millimetres.

Please implement this fix as soon as possible as there are many more fundamental mechanics to fix, and I would like to get through them before the next semester of university starts in September. If you have any questions, message A1exAndro#2738 on Discord.

[A1ex-Andro]

@Muushy The second half of this post has been changed. Please re-read it. Attached below is a simple Excel spreadsheet that takes the parameters that the user should specify (green cells), and outputs what the game should display/use (yellow cells). Torsion Bar Calculator.xlsx

[A1ex-Andro]

Since there is a limit to how much you can twist something before it irreversibly deforms and then breaks, the maximum bump stop angle can be calculated. The angle in degrees is: θmax = τmax*2L/(Gd)*180/π - β Assume τmax = 1000 MPa. Make sure G is in MPa here as well (G = 78000 Mpa).

Knowing the rest angle θ, bump stop angle θmax, rebound angle β, and swing arm length l, you can now calculate the positive vertical travel: = l*(sin(θmax) - sin(θ)) As well as the rebound travel: = l*(sin(θmax) + sin(β))

Attached below is the updated Excel spreadsheet that includes the calculation of max bump stop angle and total vertical travel. Torsion Bar Calculator v2.xlsx

[A1ex-Andro]

The previous comment and attached spreadsheet have been updated to show the positive vertical travel and rebound travel separately. More output parameters that are commonly used to evaluate the characteristics of the suspension will be added later after the previous ones are implemented.

[A1ex-Andro]

I'd also like to add that in addition to the spring torque, there is also the viscous damping torque. The damping torque is proportional to the angular velocity (in the same way that the spring torque is proportional to the angular displacement), and related by the damping coefficient (usually denoted by the letter 'c'). Like the spring torque, it opposes the direction of motion. For convenience, a dimensionless parameter called the "damping ratio" is defined, denoted by the Greek letter 'ζ', having a range of 0<ζ<1 (or from 0 to 100%) for "underdamped" motion. To provide this damping ratio, the required damping coefficient can be calculated, c=2*ζ*sqrt(k*m) where k is the spring rate and m is the sprung mass (for the individual wheel, so divide the total mass by the number of wheels here). Of course, you could let the user specify the damping constant directly, but then the range of the slider would have to vary considerably between different tanks. The damping ratio on the other hand may not need to be changed at all, so it's more convenient to use.