Thrust required to propel an AUV?

[EliotBR (Eliot)]

Hi @wolfmountain97,

Initial Estimate

Vehicle motion is governed by applied forces, and the maximum velocity at a given thrust occurs when the thrust force is equal to the drag force in the opposite direction.

F_{thrust} = F_{drag}

The thrust force (F_{thrust}) can be roughly taken from the T200 performance specs, noting that the achievable thrust is affected by thruster placement and vehicle shape (which can affect the water flowing into the thruster(s)), and thruster orientation (e.g. if the thruster isn’t pointing in the motion direction, then that needs to be factored in \rightarrow F_{thrust-forwards} = F_{thrust} \cdot \cos(\theta), where \theta is the thruster angle away from forwards).

The drag force (F_{drag}) is determined by the drag equation:

F_{drag} = \frac{1}{2}\rho v^2C_DA

where \rho is the water density you’ll be operating in, v is the flow velocity of the vehicle relative the the water (including any currents), A is the vehicle cross-sectional area in the flow direction (A=\pi \frac{d^2}{4} given dome diameter d when the flow is directly towards the vehicle front, i.e. the vehicle is moving directly forwards and isn’t going through sideways current), and C_D is the vehicle’s drag coefficient in the direction of motion.

Drag coefficient is the most difficult to determine accurately, but this textbook reference says an ROV generally has a drag coefficient between 0.8 and 1 (excluding tether drag, which presumably you won’t have for an AUV) - hopefully that’s at least sufficient for rough calculations (although those aren’t numbers I’ve verified).

When that’s rearranged you end up with

v_{max} = \sqrt{\frac{8\cdot F_{thrust}}{\rho C_D \pi d^2}}

where the vehicle is assumed to have a flow direction that’s directly forwards.

Further Considerations

Safety

It’s worth noting that T200s and the control electronics aren’t designed/intended to be run at maximum thrust for very extended periods, particularly if you’re running at the maximum voltage (they can end up overheating and become damaged).

Depending on the number of thrusters in active use, batteries can also overheat if the discharge current is too high for too long. Batteries generally have a burst current rating, as well as a continuous current rating, and as an example from our battery product pages:

@Blue Robotics 4S Battery - Discharging

Note that the maximum safe discharge rating is dependent on adequate cooling to keep the battery below 60°C. If used in an enclosed space without airflow, constant current draw must be decreased appropriately to to keep the battery at a safe temperature. For example, in a BlueROV2 we recommend keeping full throttle thruster bursts at 100% gain to no more than 30 seconds each to keep the battery at a safe temperature and allow it to cool.

It’s generally possible to measure battery temperature (and probably recommended if you’re using automated control), but it’s good to know about as a potential source of the system “maxing out”.

More Accurate Estimation

For increased calculation accuracy it may be important to consider the effects of battery discharge (reducing voltage) over time, and to take drag measurements instead of making rough assumptions about the coefficient.

The initial speed estimate above is calculated from a steady-state perspective, but in reality the vehicle will take some amount of time to accelerate to that velocity from stationary. If the transient time to change speeds becomes important you’ll have F_{thrust} - F_{drag} = m_{vehicle} \cdot a, but because drag depends on velocity that requires an integration/simulation to compute over time (that’s not particularly difficult to set up, just something to be aware of).

---

As a general note, posts with the vehicle-design tag may be worth having a look through.

Hopefully that gets you off to a decent start - feel free to post follow-ups on your progress, or any further questions you might have