Sea-Terrain Analysis ROV - An Open Development Project

[EliotBR (Eliot)]

Mass Capacity Estimation

One of the simplest checks for concept viability is the mass capacity. If the form-factor isn’t capable of supporting the required components then it’s not a valid design, so this is a reasonable check to perform early on in the process.

Concept Constraints

The two current concepts are both based on cylindrical enclosures, which are sized based on what is already available in the BR store (as a reasonable starting point, and to make use of the costs that are reduced by scale-production). The first concept uses parallel 4" tubes in a catamaran structure, whereas the second one uses a 4" tube inside an 8" tube, forming a donut. It’s conceivable that a catamaran-style ROV could instead use 3" tubes, but the donut tube diameters are relatively fixed by the thruster size and the requirement to have at least some space for the electronics and batteries inside.

Mass Minimisation

Since this design isn’t intended as a highly modular platform for others to build off, it makes sense to try to avoid material that’s only there for buoyancy or ballast purposes. Additional buoyancy can be achieved by lengthening the tubes, which in turn provides extra space for the contents and wiring. If extra mass is desired then likely more batteries can be included.

Avoiding buoyancy material/ballast also helps to minimise the overall mass of the vehicle, which is beneficial for efficient motion. Adding buoyancy foam still adds to the total mass and drag, which takes more energy to accelerate than a smaller total mass, particularly given the fixed thruster size.

Wet vs Dry Mass

From a buoyancy standpoint, it can be helpful to consider “wet mass” and “dry mass”. Components inside the enclosure don’t contribute to the buoyancy, so their total (dry) mass is considered. Components outside the enclosure do partially contribute to the buoyancy, so it can be helpful to consider them by the equivalent mass of their gravity force minus their buoyancy force (so-called “wet mass”). If this wet mass is known, the overall buoyancy balance can be considered as buoyancy from the total enclosed volume, minus the dry mass of everything inside enclosures and the wet mass of everything outside it/them, which is a convenient simplification.

Neutral Buoyancy Calculation

The buoyancy force of a given volume in a fluid is calculated by the displaced fluid volume, multiplied by the fluid density and gravitational acceleration:

\begin{align} F_{buoyancy} &= V\cdot\rho\cdot g\\ &= m_{displaced} \cdot g \end{align}

If we aim for neutral buoyancy, we want

\begin{align} F_{buoyancy} &= F_{gravity}\\ m_{displaced} \cdot g&= m_{total}\cdot g\\ \rightarrow m_{total} &= m_{displaced}\\ \rightarrow m_{capacity} &= m_{displaced} - m_{required} \end{align}

where m_{required} is an optional offset for the mass of the known components (e.g. thrusters, end caps, tube material per unit length, sonars), leaving the ‘capacity’ as the mass of the unknowns/variable inputs (electronics, cables, batteries, etc).

Applied Calculations

In the interest of simplicity, and a conservative estimate for capacity, the displaced water is assumed to be pure, with a density of 1\text{g/cm}^3.

The catamaran volume is roughly determined by two cylinders of equal length

\begin{align} V_{catamaran} &= 2\cdot\pi r_c^2l_c \end{align}

The donut volume is determined by the outer cylinder minus the inner cylinder

\begin{align} V_{donut} &= \pi (r_o^2 - r_i^2)l \end{align}

From the relevant technical details:

\begin{align} r_c &\approx 57mm\\ r_i &\approx 50.6mm\\ r_o &\approx 108mm\\ \rightarrow V_{catamaran} &\approx 2\pi \cdot 57^2\cdot l_c\\ &\approx 20414.07\cdot l_c &[mm^3]\\ \rightarrow m_{displaced-catamaran} &\approx 204.14 &[g/cm]\\ \rightarrow V_{donut} &\approx \pi(108^2-50.6^2)l\\ &\approx 28599.93\cdot l &[mm^3]\\ \rightarrow m_{displaced-donut} &\approx 286.00 &[g/cm] \end{align}

For the expected mass:

item	dry mass	wet volume	wet mass (fresh)
4" flange	144 g	6 mm	83 g
4" dome	82 g	~275 \text{cm}^3	-193 g
4" 10 hole end cap	159 g	6 mm	98g
4" tube	25.7 g/cm	-	-
8" flange	690 g	6 mm	470g
8" acrylic end cap	564 g	13 mm	88g
8" tube	50.2 g/cm	-	-
T200 thruster	-	-	156 g
Ping360	-	-	175 g
Ping Sonar	-	-	55 g

Each concept design includes 3 thrusters and one of each sonar (3\times 156 + 175 + 55 \approx 700g).

In addition, the catamaran design includes 2 4" domes, 4 4" flanges, and 2 4" 10 hole end caps (~140g). The donut design includes 2 4" flanges, 2 8" flanges, and 2 8" acrylic end caps with a hole in the middle (~1245g).

Accordingly,

\begin{align} m_{capacity-catamaran} &\approx (204.14 - 2\cdot 25.7)\cdot l_c - (700 + 140)\\ &\approx 152.74 \cdot l_c - 840\\ m_{capacity-donut} &\approx (286.00 - (25.7 + 50.2))\cdot l - (700 + 1245)\\ &\approx 210.10\cdot l - 1945 \end{align}

Those expressions can be plotted as follows:

The main remaining weight is from batteries and internal electronics (e.g. companion computer, autopilot board, ESCs, mounting hardware). Taking a 1163g Blue Robotics Battery as a rough upper limit of battery weight, and (conservatively) assuming a similar weight for the combined electronics and mounting, both designs would be neutrally buoyant with a tube length of somewhere around 20cm. That doesn’t seem unreasonable as an initial size estimate, so both designs are considered feasible for now, and can continue to be evaluated.