T200 PWM and current relationship

Blue Robotics Products Thrusters and Motors
1

I have a underwater quadcopter using T200s. I ran two tests on it, one with set up with lots of drag and another with less drag. In the test I ran with drag, I sent the max PWM signal and it reached a speed of 6 ft/s and the motors pulled 60 A. On the test with less drag, I sent the max PWM signal again and it reached 8 ft/s and the motors pulled 70 A. My question is why would the current draws be different in these tests? Does the PWM control the current the motors draw or is the current the motors draw dependent on how fast it spins?

Any insight on this relationship would be appreciated.

Thanks!

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Hi @luisquint -
That sounds like a cool project!
The servo-style PWM signal does not correspond to motor rpm, but instead governs how much current the ESC will use to try and reach a given RPM. You sent the same signal in both tests, but when going faster, you’re using more energy, and the lower drag allows the system to reach higher speeds. The relationship between current consumption and PWM signal varies depending on how you’re using the motor!

Does your quadcopter fly in the air? Note that T200s should not be run in air for more than a few seconds…

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@tony-white Can you expand further on this, because @luisquint has asked a question that I’ve never quite resolved completely. Even in the process of rewriting this post several times.

  1. Let’s just for moment ignore the body drag of the rest of the platform. Does 1N of thrust in a stream moving already at 1m/s cost the same current at 1N of thrust at rest? I’m assuming that generating 1N requires an excess stream velocity that is added to the velocity of the water already moving by. Let’s say for argument that on a T200, 1N requires an additional 0.5m/s. So at rest we need to make RPM so that (given slippage angle on the prop) we get 0.5m/s flow. If we were already moving at 1m/s we’d need RPM to generate 1.5m/s flow to get 1N. And I think that in both cases the current consumption is the same, so in the P = Fv equation, the v corresponds proportionally to the additional velocity imparted to the water.
  2. Then when we add body drag back into the picture we need more thrust at high speeds (linearly for laminar flow and squared as it breaks into turbulence) and there’s the cross section (A) and the Coefficient of drag (Cd), and F = v A Cd, if I recall.

But after all that, I still don’t understand why in @luisquint ‘s test for the same PWM setpoint, giving the same current set point, the higher drag would result in a higher current. I would have expected from your description (and my rambling) that the resulting speed would be less but that the current would be the same.

Side question: Is the what looks like quadratic relationship in the Current Draw vs PWM graphs in the T200 technical section just a mapping from the PWM value to an internal current setpoint, or is it something physical?

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Hi @psupine -
I’m no expert (we’d need to find a naval architect) but what you’re saying sounds mostly right.

In Luis’s test, in the high drag coefficient configuration, the props were not acting as efficiently. If slip was 0, you could know the speed through the water based on the RPM. But because there is slip, and that slip increases when the prop is prevented from moving through the water (by body drag), efficiency drops and you use more current - “spinning your wheels”.
In the low drag case, the prop can move closer to its no-slip speed through the water, and so spin faster, and propel the vehicle to a faster speed. That extra speed does take more power, even though the pwm throttle setpoint is the same. You’ve got traction, and aren’t doing (as much) of a burnout.
You can kind of think of it as a car that is geared for speed (not torque) trying to reach a top speed. Your ferrari with a trailer hitch and boat behind it may only reach 50mph with the throttle wide open, but the engine isn’t at its max rpm, or a particularly efficient operational point - it isn’t able to make maximum power at the lower rpm with that much opposing torque (especially if you’re in the wrong gear - dictated by prop geometry in the marine case)
With the trailer off, it can better cope with the loads and speeds it was designed for, and so go very fast with the petal to the metal! It will of course use more fuel at the higher speed / rpm / power output.

As for the parabolic shape of the PWM vs. current, I believe this is due to the firmware - for a given PWM value, the ESC is trying to achieve a current along that curve. If the operational situation prevents it from doing so (high drag case) it does the best it can. When better able to put the power down, for the same PWM value it thus reaches its desired current (or closer to it at least.)

It’s worth noting that the data in that curve was taken in a test tank, with the motor not allowed to advance - so the slip is 100%! Thus, I’d assume that on a moving vehicle, the thrust for a given pwm may be a bit lower, as well as the current, but the efficiency will be higher!

If we assume Luis’s vehicle has 4 motors, then 15A a t full throttle isn’t as high as the T200 does at 100% slip - that’s closer to 24A at 16V. In the low drag configuraiton, he gets 17.5A per motor - still lower, but approaching the maximum speed thru water that the pitch of the prop can provide. With 0 drag, there is no slip, and the max speed from a T200 would be rpm * fwd_distance_per_revolution - this is somewhere around 4 m/s? However in the case of the BlueBoat, hull-speed starts to make things take exponentially more energy closer to 3 m/s…

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Yeah, I think the whole Ferrari (*) gearing angle is absorbed by choosing a particular prop pitch. High gear is the equivalent of being over pitched and you sit there cavitating (or burning the clutch) without being able to convert the effort into motion. But given a certain physical pitch angle on the prop blades, there is an RPM that hits the incoming water stream (at whatever velocity) that corresponds to a certain slip angle … mostly, I think (?). Or maybe not.

If you have a very flat prop, optimised for low speeds, spinning it ludicrously fast might not be an option; at some point, you can’t. Conversely, if you have a prop designed for high speed … arhh … it simply can’t generate much thrust at low RPM. Efficiency is not just an RPM tradeoff.

I used to have a textbook on propeller design. I wonder what I’ve done with it, but clearly I need to read it again.

(*) I remember my then two year old daughter, the first time she saw a Lamborghini up the street, asked me if it could tow a caravan.