In a recent thread, some discussion about torque and "torque slew rate" came up. I thought the discussion deserved a separate thread. This may be all wrong, but I'll go first:
So what is “torque” anyway?
Torque is a rotational force; a force which (in sim racing) is applied perpendicular to the radius of a steering wheel. It’s what your wheelbase applies to turn the wheel or resist your hands as you are also applying turning force (also torque) to the wheel.
So what’s a Newton-meter (Nm), the unit of torque? Let’s start with “what’s a Newton?”
A Newton (N) is a unit of force. It’s the amount of force required to accelerate one kg of mass at the rate of 1 meter per second squared.
Because the time (seconds) is squared, we are talking about acceleration, not velocity.
Now let’s take a look at how torque, denoted as tau, with units of Nm (Newtons*meters), is applied in the sim racing world. We need to know three things: The wheel radius, its mass ("weight") at its radius, and the torque applied to it.
(1) Let’s say your wheel is 30 cm in diameter (quite typical). So its radius is 0.15 m.
(2) Let’s say for a typical wheel and button box combo, we call the lumped mass at the rim's radius to equal 0.5 kg.
(3) Let’s say you have a wheelbase set to apply 10 Nm torque.
How much force is applied at the rim? Equivalently, how much force must you apply to prevent the wheel from turning? Assuming that the torque is always applied perpendicular to the radius of the rim (as is normal in sim racing):
Torque (tau) = radius (r) * force (F)
Or:
(10Nm)=(0.15m)*F
We want to solve for the force F, so:
F=(10Nm)/(0.15m)=66.67N
For those accustomed to English units, one Newton equals about 0.225 pounds (of force, not weight!), so that’s about 15 lbs of force spinning madly while you wrestle it.
Given this force, how fast will the wheel be turning, starting from a stand-still, after one second?
F=mA
So, solving for the acceleration A:
A=(66.67 kg*m/s^2)/(0.5 kg)=(133 m/s^2)=(436 ft/s^2)
If s=1 (one second), then that’s 436 ft/s velocity, which equals 297 MPH!!!
Well, OK, that’s probably not going to happen, because the motor has some maximum speed of operation that is likely to be considerably lower (e.g., the electrical impulses that activates the motor are only so frequent at their peak, and the motor won’t go faster than that).
One take-away from the above is that the maximum torque (when freely spinning unopposed) can only be applied for a very short time (likely less than one second) before the system has no choice but to reduce the applied torque to close to zero, i.e. once maximum RPM is reached. But needless to say, the wheel can turn very, very quickly and with a lot of force applied at the small radius of a typical wheel. And that’s with “only” 10 Nm applied torque. No wonder people can hurt themselves with these wheels!
Now let’s look at “torque slew rate.” This is a figure of merit supplied by at least one manufacturer (SimuCube). This is presumably the maximum rate at which the applied torque can change. Their three systems are noted as having:
Sport: 17 Nm max, 4.8 Nm/ms slew rate
Pro: 25 Nm max, 8 Nm/ms slew rate
Ultimate: 32 Nm max, 9.5 Nm/ms slew rate
Unless artificially limited in firmware, one might expect slew rate to be directly related to max Nm. And indeed this is roughly true, e.g. how long does each take to reach maximum torque from a standstill?
Sport: 17/4.8=3.5ms
Pro: 25/8=3.1ms
Ultimate: 32/9.5=3.4ms
So all three can theoretically reach their maximum torque in about 3.3 ms. A rapid maximum-force tank-slapper (+max to –max torque in a few ms) would likely be very difficult to control.
In any event, the actual achievable torque slew rate is dependent on the limits of the motor itself, the wheel-base’s firmware limits, any in the OS, any particular game’s feedback limits, and the weight and diameter of the wheel and button box, whose moment of inertia opposes acceleration.
So another take-away is that, for maximum sensitivity in force-feedback, you should prefer a light-weight and small-diameter wheel.
I hope this is a helpful starting point. It's semi-likely that I've made an egregious mistake somewhere, so please point out any errors (gently). I reserve the right to fix errors in this post. Thank you.
Updated to fix various errors thanks to Neilski (hopefully without introducing too many new ones!). Thanks!
So what is “torque” anyway?
Torque is a rotational force; a force which (in sim racing) is applied perpendicular to the radius of a steering wheel. It’s what your wheelbase applies to turn the wheel or resist your hands as you are also applying turning force (also torque) to the wheel.
So what’s a Newton-meter (Nm), the unit of torque? Let’s start with “what’s a Newton?”
A Newton (N) is a unit of force. It’s the amount of force required to accelerate one kg of mass at the rate of 1 meter per second squared.
Because the time (seconds) is squared, we are talking about acceleration, not velocity.
Now let’s take a look at how torque, denoted as tau, with units of Nm (Newtons*meters), is applied in the sim racing world. We need to know three things: The wheel radius, its mass ("weight") at its radius, and the torque applied to it.
(1) Let’s say your wheel is 30 cm in diameter (quite typical). So its radius is 0.15 m.
(2) Let’s say for a typical wheel and button box combo, we call the lumped mass at the rim's radius to equal 0.5 kg.
(3) Let’s say you have a wheelbase set to apply 10 Nm torque.
How much force is applied at the rim? Equivalently, how much force must you apply to prevent the wheel from turning? Assuming that the torque is always applied perpendicular to the radius of the rim (as is normal in sim racing):
Torque (tau) = radius (r) * force (F)
Or:
(10Nm)=(0.15m)*F
We want to solve for the force F, so:
F=(10Nm)/(0.15m)=66.67N
For those accustomed to English units, one Newton equals about 0.225 pounds (of force, not weight!), so that’s about 15 lbs of force spinning madly while you wrestle it.
Given this force, how fast will the wheel be turning, starting from a stand-still, after one second?
F=mA
So, solving for the acceleration A:
A=(66.67 kg*m/s^2)/(0.5 kg)=(133 m/s^2)=(436 ft/s^2)
If s=1 (one second), then that’s 436 ft/s velocity, which equals 297 MPH!!!
Well, OK, that’s probably not going to happen, because the motor has some maximum speed of operation that is likely to be considerably lower (e.g., the electrical impulses that activates the motor are only so frequent at their peak, and the motor won’t go faster than that).
One take-away from the above is that the maximum torque (when freely spinning unopposed) can only be applied for a very short time (likely less than one second) before the system has no choice but to reduce the applied torque to close to zero, i.e. once maximum RPM is reached. But needless to say, the wheel can turn very, very quickly and with a lot of force applied at the small radius of a typical wheel. And that’s with “only” 10 Nm applied torque. No wonder people can hurt themselves with these wheels!
Now let’s look at “torque slew rate.” This is a figure of merit supplied by at least one manufacturer (SimuCube). This is presumably the maximum rate at which the applied torque can change. Their three systems are noted as having:
Sport: 17 Nm max, 4.8 Nm/ms slew rate
Pro: 25 Nm max, 8 Nm/ms slew rate
Ultimate: 32 Nm max, 9.5 Nm/ms slew rate
Unless artificially limited in firmware, one might expect slew rate to be directly related to max Nm. And indeed this is roughly true, e.g. how long does each take to reach maximum torque from a standstill?
Sport: 17/4.8=3.5ms
Pro: 25/8=3.1ms
Ultimate: 32/9.5=3.4ms
So all three can theoretically reach their maximum torque in about 3.3 ms. A rapid maximum-force tank-slapper (+max to –max torque in a few ms) would likely be very difficult to control.
In any event, the actual achievable torque slew rate is dependent on the limits of the motor itself, the wheel-base’s firmware limits, any in the OS, any particular game’s feedback limits, and the weight and diameter of the wheel and button box, whose moment of inertia opposes acceleration.
So another take-away is that, for maximum sensitivity in force-feedback, you should prefer a light-weight and small-diameter wheel.
I hope this is a helpful starting point. It's semi-likely that I've made an egregious mistake somewhere, so please point out any errors (gently). I reserve the right to fix errors in this post. Thank you.
Updated to fix various errors thanks to Neilski (hopefully without introducing too many new ones!). Thanks!
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