# Looking for basic power formulas for electric drive...

Discussion in 'Propulsion' started by JunkRat, Jan 27, 2019.

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### JunkRatJunior Member

Been researching electric vessels. Found the Silent 55 which is pretty fascinating. I feel the Tesla of boats is not quite viable yet. But I'd like to understand some basics of power costs.

Observing fuel efficiency of motor yachts and catamarans there are so many variables that it is hard to derive the formulas for how much power is required to move a boat that weighs X and is length Y at speed Z.

I have observed that longer and heavier boats are less fuel efficient. (But larger boats would also have more space for solar panels)

Am I correct in assuming that a monohull trawler and a sailing catamaran are both "displacement" vessels? Because neither has a hull that's planing.

I've also observed that planing hulls and hydrofoil boats do not seem to get significant efficiency boosts while up out of the water, though they can go a lot faster.

So there are probably three different possible formulas:
1. Displacement power required
2. Planing power required (lets just assume a basic planing hull as efficient as was common in planing boats 30 years ago.)
3. Foiling power required

I have an engineering background and can teach myself, so feel free to point me to books on the subject. Looking for targetted stuff, though, I don't want to learn how to design hull forms... if I put these ideas into practice, I'll buy an existing boat and be repowering it. That's in my wheelhouse totally.

Thanks!

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### jehardimanSenior Member

There is so much wrong with your thinking I don't even know where to begin...except at the modern von Kármán–Gabrielli diagram. Longer and heavier boats are always more fuel efficient per Kg moved. And overall power efficiency is nuclear ->fired steam ->internal combustion -> electric in that order at the present time. At the present moment, electric power densities can approach internal combustion engines for several minutes. Totally useless as a prime mover, especially for hydrofoils...see the von Kármán–Gabrielli diagram.

I'm not just being negative, but I see this again and again...someone draws an unrealistic boundary on the whole energy problem. If you charge your Tesla car from a 40% efficient coal fired power plant is that better having a 70% efficient ICE? NO! Is spending 1M kW/hrs to make a battery that over it's lifetime will deliver 100K kW/hrs a good thing? NO! Is running a hydrogen fueled car from nuclear plant producing hydrogen and O2 a good thing? YES! There is so much misinformation and NIMBY out there that these types of posts just seem so strange to us engineers who have had to do the analysis. Almost like having to listen to political diatribes on full volume.

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### xellzSenior Member

I'm also thinking about electric propulsion myself. Although there were some major delays with boat plans i hope i can finally put my ideas into action this spring. I tried my best to get all information together to see if it's viable choice or not. In short what i found, if compare cost to performance only, it's not viable for majority of applications (my case is probably one of few exceptions). It's too expensive with a lot of compromises.

If re-powering existing boat, look for data on speed, rpm on engine and fuel consumption then compare to power curves of said engine. That's how i got rough estimation myself. Probably more reliable source for power requirement since it does include winds and less that perfect weather conditions. There aren't many electric boats out there yet and even less people share their experience. Planing boats are probably out, too short run-times.

What size of a boat you're looking at? I saw Silent 55 too and i think that's where electric does make sense, slow, but noise, vibration free and a lot less maintenance to worry about. If it will be used most of the time of course. Silent 55 way out of my league, i found quite nice electric conversion that would make sense for normal people. Previously sail boat, 9m x 2.8m and weight about 1.8t from description. At 5 knots consumes most of the time about 2kw. Has 1.2kw worth of solar panels that actually look quite nice on the boat.
Look from above

and a record of power consumption with speed readings

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### philSweetSenior Member

You need to nail down two concepts at the very get-go. The first is energy density. This is the energy capacity of the "fuel tank", be it a diesel tank, cord wood storage, or batteries, divided by the volume you need to set aside for it. In the case of tanks, they can be molded to make use of odd shapes, but usually you just have a box and have to fit it into a non-box volume in the hull. Batteries need to be taken as a system which includes the battery boxes and interconnects and BMS and charging systems. Batteries take up a lot more space than a diesel tank. You can google charts of energy density for storage systems. A related, and frequently confused idea is specific energy. Specific energy is the capacity divided by the mass of the storage system. Batteries are also worse than diesel in this metric. So decide how much fuel energy you want to have on board, and think about the space in the boat needed to accommodate it. Real estate on boats is expensive. If you have to build a bigger boat to fit the batteries, figure out what an additional sqft of floor space costs you. This is the part that seems to be the hardest to grok for newcomers who are used to electrical energy just flowing out of outlets, without really understanding the comparative values of stored energy systems. This is what you need to research first.

The second concept, which is 100% independent of the first one, is power density. This is the easy part on the surface of things, but there are some subtleties that differ between electrics and ICEs. Again, it is the hp rating divided by the volume set aside for the system. Normally, you would include the diesel and its ancillaries and exhaust and cooling systems. For electrics, you have the motor, controller, and cooling systems. For electrics, these basically scale with amps, so higher voltages yield better numbers. Both diesel and electric scale roughly with 1/rpm, so faster is better. Specific power is the rated power divided by mass.

Establishing the rated hp and energy storage requirements lets you estimate the volumes and weights of different systems. Looking at fitting the components into a general arrangement, you can get a footprint also. Footprints are another challenge batteries face when compared to tanks.

Endurance is just capacity/power. Except this doesn't work because you don't run full throttle all the time. So you need an actual operational envelope that defines how much time is spent at each power level on each sortie. This is where the actual engineering lies. These can't be looked up on the web. They can be absolutely anything. For recreational craft, there really isn't an answer to this. For charter craft or tour boats, you can at least put some bounds on this space. Because this is the fuzziest of the design criteria, we have to build in some slop somewhere. Either less hp or more capacity. Marketing considerations usually eliminates the former. For fast ships, they do have the option of slowing down to conserve fuel. But this is far less effective for slower ships. If you find yourself pushing against a 20 knot headwind coming back from a fishing trip, there is nothing a 10 knot boat can do to reduce fuel consumption. So lower performing vessels require a considerably larger reserve capacity than a quicker vessel. And thus the vicious cycle begins.

The power densities, specific power, and cost per power performance of diesel and electric are much closer to each other than the energy density, specific energy, and cost per energy performance of the two - electrics being either about an order of magnitude worse or an order of magnitude more expensive. So you want to look at operations that have very low endurance. As jehardiman suggested - minutes, not hours.

Recharging a diesel tank is reasonably straightforward and standardized for small craft. You get between 5 and 10 gallons/minute at the pump, or a couple of tons from a delivery truck if you are a sport fish or tour boat. The delivery process is 100% efficient (you get back everything you paid for). Lets say you have a 50Amp shore connection delivering 220V to your boat. What is the equivalent gpm in diesel? Figure 90% available to the charger, 90% efficiency for the charger, and 90% efficiency for charge uptake in the battery. Can your battery configuration actually absorb this amount of power? Does it have to taper off for last 20%? How long will your battery take to recharge if it replaces the equivalent of 50 gallons of diesel and ends up at 100% charge? The recharging phase of vessel operations is often the limiting factor and overall driver when considering what battery technology to use.

Battery replacement. Look at a simple life cycle cost model that includes the price of fuel, maintenance expenses, and battery replacement in the case of electrics. What I typically find is that the cost to replace the batteries is about the same as the cost to buy an amount of diesel equivalent to the total electrical energy that has passed through the batteries during their useful life. So basically, even if you get the electricity for free, you still pay about the same amount for energy long term.

Look up Ragone charts for an overview of these performance characteristics. They come in different flavors as far as energy density, or specific energy, or endurance-oriented versions. There's no easy way to do this except sit down and design systems that work as a whole, then look at the cost, size, weight, and general arrangement that is required.

The ship resistance parameters that you asked about are the one simple part of this. They can be estimated quite accurately for any given normal shape. But you usually have to supply a weight, so it becomes iterative in the case of electrics because of the weight of the storage (which doesn't change with consumption, making performance more sensitive to it). Most methods are particular to certain classes of ships and speed ranges, but they are all covered. These should be considered minimums or ideals. Wind and waves play an ever increasing role as ships get smaller and slower. Google ship resistance and powering. And there are several charts floating around this site as well.

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### xellzSenior Member

Maintenance is also major cost factor that i would add. When i was considering initial price and cost of use for me electric makes sense not only for low noise and no smell, but also financially. I'm expecting over 2000h yearly and use is mixed, mostly go slow, drifting with engine on, occasional fast(relative of course) short distance move. Recent batteries show long cycle life 5000-10000 to 80%dod. But rapid charging greatly reduces those numbers.

But i sure agree that even with best currently available batteries there are far toomany limits on electric before even touch the topic of price.

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### JunkRatJunior Member

Phil, nothing in your comment was new to me. I'm well aware of all of those issues, and its all irrelevant because like the other guy you're making a whole bunch of assumptions, one of which is that I'm building a battery based boat and the other that I don't know what a BMS is, etc. I know all of that, better than %99 of the population.... and I never said I was building a boat. I'm an engineer testing a hypothesis, my "project" is not a boat, but some math and so I just asked for the formulas to calculate the energy needed to move a hull at a given speed... I'm ok with basic assumptions like, zero wind, waves, etc. People sizing a diesel engine for a boat must calculate which engines will provide the power they need, and they don't just throw their hands up because they don't know what the wind will be.

But hey, at least you tried to help. Despite making those assumptions you tried to answer them... but I would like a pointer to an answer to my real question.

If there aren't formulas, I can get statistics for a given boat's energy usage at various speeds. From that I can calculate the energy used by taking the GPH of diesel... But what is the efficiency of a modern Volvo diesel engine? (Or other brands if you have numbers handy.)

ALL I'm asking is how to calculate the energy needed to move the boat. (Lets assume there is sufficient torque as electric motors produce torque well.)

Thanks xellz. I'm not looking to repower a boat, or looking at a specific boat. I have some performance numbers for various boats from manufacturers. If there aren't formulas to derive the required energy, I can use those numbers to get a back of the envelope number.

Like I said, I'm an engineer doing research. I'm looking for the numbers I need to check a hypothesis. I'm not working on a project. If those numbers check out, and what they say, that will indicate the direction for another hypothesis, that might ultimately result in a project.

Last edited: Jan 27, 2019
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### gonzoSenior Member

It is rather straightforward. You calculate or measure the resistance of the boat at different speeds. That gives you the power required to propel the boat at each speed. Divide those values by your efficiency ratio and that gives the power output required of the motor.

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### Ad HocNaval Architect

As already noted (expertly) by Phil and JEH, that is the easy part. Basic Naval Architecture - resistance and propulsion.

You have not stated what your hypothesis is...!

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### philSweetSenior Member

There are some fairly quick and dirty methods that let you make some guesses or measurements about the hull form and desired speed which then spit out a power. These have quite a few built in assumptions though, which may be why there has been some reluctance to provide them. We are used to being given a better idea of the craft, and therefore can better judge whether the method will work.

For instance, some of the seat of the pants estimates assume a prop efficiency of 55%. That is a good, practical, economical figure for conventional power. But for electric power, the trade-offs on cost would favor a more expensive and efficient prop.

So if you give us an idea what the hypothesis is, we can suggest a type of hull form and powering formula, and also comment on the assumptions in the model. If you want a comparison with something such as an ICE powered vessel, just pick one.

Catamarans can be displacement, semi displacement, or planing, just like monohulls. However, the narrower hulls need to be accounted for in deciding which type it is. They transition differently than monohulls because typically they have lower beam/length and lower displacement/length ratios.

Dave Gerr's Propeller Handbook covers basic powering formulas, discusses some of the assumptions in the formulas, and covers props and shafts. Electrics tend not to want to be in the middle of the design space depicted for ICEs. But they will be on the charts somewhere, usually tucked in a corner.

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### DejaySenior Newbie

I would love to learn more about power requirements for a lightweight catamaran, something like 2.5t displacement and 25-30 feet.

Is there something like a standard series of measurements for a specific catamaran hull form that gives total resistance at a certain speed? Some chart with experimental readings for a modern efficient displacement catamaran hull given length and displacement? Or is the only feasible way learning yourself and use simulation software like free ship or delftship?

Regarding hydrofoils, the "minimum foil power" is I think easier to calculate because you can largely ignore wave mechanics. I've bought the book "Hydrofoils" by Ray Vellinga and it does contain formulas to calculate lift, drag, power and speed but I've only skimmed it. My guess is that for low power density of electric you'd need to make the foils very large to generate enough lift at low speeds, and then the drag of the foils, the additional weight for structural integrity and control mechanisms and the costs negate any advantage.

BTW it seems the Silent 55 is the same boat as the SolarWave 54.

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### gonzoSenior Member

You can look at similar boats as a starting point. If they have measured values, that is speed vs power, etc. then you can compare your calculations to that. In general, boats that have conservative shapes and weights will behave in similar manner.

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### DejaySenior Newbie

Gonzo I'm not sure if you can actually find numbers of "total hull resistance" or "propulsive power" for similar boats. I'm a newbie so maybe it's just that I don't know how to find them, but what I did find is notoriously either for the wrong class of boat (e.g. much larger and heavier) or you get imprecise anecdotal evidence of how much you throttle you need to push you 60HP outboarders which includes unknown inefficiencies for motor and propeller. For planning an electric conversion for a say 30' to 44' power catamaran these numbers don't seem to be very helpful.

What I did find (@JunkRat) is three easy ways to estimate total hull resistance for displacement vessels. There is hullcalc.xls which is the easiest to get an estimate of propulsive power you need to reach a certain speed. The other is delftship that uses some series from the university of delft. The third is michlet which is a bit harder to use but seems to do the most elaborate simulation and optimization of hull shapes including wave interference. There is also free computational fluid dynamics software based on openFOAM which is super complicated. Which probably explains why there is less interest in some "general formula" to estimate ship resistance because CFD is the way to design a boat seriously. It really is more complicated than rocket science!

For example throwing some numbers into hullcalc.xls a 12m catamaran with 1m wide hulls and 6000kg full loaded displacement would need 1.5kW at 6 knots, 4.7kW at 8 knots and 13.4kW at 10 knots. If you have 50% efficiency from input power to propulsive power like torqeedo e.g. claims you need double that out of your battery or generator. A 2.5m longer catamaran with the same displacement would still need 1.24kw at 6 knots but only 7kW at 10 knots. A monohull would have to be ridiculously longer to achieve the same energy efficiency.

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### gonzoSenior Member

What is the type of boat you are proposing? It is impossible to give you much relevant information otherwise. However, there is a fair amount of published data for sailing catamarans under power.

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### DejaySenior Newbie

Just trying to understand some basics on the electric power requirements for boats. Still have a lot to read and work out before I propose anything

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### gonzoSenior Member

OK. If you replace an internal combustion engine for an electric motor, and the weights don't change, you simply specify the same power.

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