Among the key questions that must be answered in any powerboat's design phase are: How much power does it need, and how far can it go between gas docks?
The Starwind 860 trimaran that I'm currently working on started life as a series of computer simulations to answer these two questions. In today's post, I'll take you through some of these calculations and the logic that led to the final choices.
We've already established that the boat needs to carry at least one tonne of cargo, to take two couples and a few kids on day and weekend trips, or to support two people for extended cruises. And we've stated that we want her to run comfortably in force 4 weather, with the ability to get home in a force 6 if necessary. That sets a pretty firm minimum size at about 1000 kg for the bare hull; we'll figure on a working displacement of 1500 kg in light-running condition and 2150 kg on a typical cruise with full tanks and a full crew. In cargo mode, we'll use 2600 kg. (The design was based around estimates close to these, but the figures used here come from a detailed weights and moments calculation based on the CAD model and specifications.)
One of my favourite little bits of code is Michlet, written by Australian mathematician and hydrodynamicist Leo Lazauskas. The program looks like something out of the DOS age and uses a finicky custom file format, but beneath its old-school interface lies a powerful optimization and hydrodynamic analysis engine that computes wave systems and resistance curves with remarkable accuracy. Michlet has the ability to compare a hundred candiate hulls in a few seconds, choose the ones that come closest to a particular performance goal, tweak their parameters a bit to spawn a hundred new hulls, and repeat until an optimal set of form parameters is found. I did this for all the use cases the Starwind 860 would see, eventually zeroing in on a suitable class of hull shapes, from which the final boat's hulls were drawn. Michlet came into play once again to verify the final design.
The raw resistance curves shown below include everything to do with the water: the wave system, the skin friction, the interference between the ama and vaka wakes, even the vacuum behind the transoms at high speed. They're not perfect, but the Starwind 860 is well within the limits of the theory on which Michlet is based. The empty, light, standard and heavy displacements are as described above: 1000, 1500, 2150 and 2600 kg respectively.
To account for wind resistance, we compute the air drag in the usual way (F = Cd * A * 0.5 * rho * V^2) and add this to the resistance of the hulls. For the Starwind 860, the frontal area is approximately 4.0 square metres. The hulls are fairly streamlined, but the crossbeams and pilothouse are not, so we err on the side of caution and use Cd = 1.1. (By comparison, a truck's Cd is 0.8 to 1.0, and a modern car like a Prius or Insight is about 0.25.)
We can then compute the power needed to propel the boat at a given speed: just multiply the speed by the resistance. The engine must produce more power than this, of course, as a fair bit is lost at the propeller when we convert from a spinning shaft to a force on the water. For a high-thrust outboard engine and large diameter, shallow pitch propeller of the type being considered here, 55% to 60% of the shaft power is actually translated into thrust. We can now calculate how much power the engine must produce to propel the boat at a given speed:
I've mentioned in previous entries that we'd like a 10 knot (~5 m/s) cruise and 20 knot (~10 m/s) sprint. We can now specify a suitable engine; a wide-open rating of 50 kW (70 hp) will give us our 20 knot sprint with a standard cruising load. If we're willing to sacrifice a bit of top end speed when loaded down, and save the fast dashes for when we're running light, we'll do quite well with 40 kW (55 hp). That's still enough for a hair under 9 m/s, or 17 knots, if we want to punch the throttle with a full crew.
To determine the fuel efficiency, we need to know something about the engine. The Starwind 860's standard spec is for a gasoline outbard of the 4-stroke or modern 2-stroke direct injected type. At this point, we have to do some hand-waving. Outboard manufacturers don't publish their fuel maps. Indeed, they rarely publish even the most basic of performance curves. So we have to make some assumptions. The brake specific fuel consumption (BSFC) of this class of engine varies considerably; it might be 250 g/kWh at the most efficient operating point, but could fall off to 400 g/kWh or worse at idle or full throttle. I'm going to assume an average of 300 g/kWh in the range of interest, and accept that there may be a fair bit of variation here.
At this point, I'm also going to convert from m/s to knots, to keep the sailors happy. The physics calculations, for which it's much nicer to stick with SI units, are over. Now we just need to figure out how much fuel she'll use. With the power curves shown above, the BSFC we've assumed, and the specific gravity of gasoline, we can calculate the fuel consumption for any speed and load condition:
If you've seen such curves before, you might wonder what's up with the straight segments on the left. Remember that we're using an outboard engine. Like all internal combustion engines, these have some minimum idle speed. As a very general rule, you can't run an engine below about 4% of full throttle without it either stalling, running rough, or running too cold to be efficient. So the Starwind 860 can't actually do 3 knots; you'd have to tow a drogue to slow it down to that speed. New direct-injection technology pushes the low idle down a bit, but it's not something we're going to count on (and who cruises for hundreds of miles at three knots, anyway?)
At its best, 5 to 6 knots, we're getting five to eight nautical miles per litre- that's roughly 10 to 6.3 L/100km in car terms, or 20 to 30 nautical miles per American gallon. Efficiency's going to fall off dramatically at higher speeds, but it's still pretty good for a boat of this size. And although it's not included in these graphs, we'd have to lop a bit more off for the added resistance in a head sea, if we're going to be beating into waves of appreciable size.
Converting fuel efficiency to range is a simple matter of multiplying the fuel consumption by the available fuel capacity. The Starwind 860 has room for a pair of 140 litre tanks. You can never get the last bit out of the bottom of the tank, and filling them to the brim is not prudent, so 90% of the available volume gives us 252 L of fuel.
This gives us a whopping 1500 nautical mile range in standard cruising configuration, if we're not in a hurry. The usual rule of one-third for the trip out, one-third for the trip back and one-third for Murphy therefore yields a cruising radius of up to 500 nautical miles, or two solid weeks of 7-hour days. That's enough to go from Gander, NFLD to the midpoint of the Labrador coast, and back. It could take us from Kingston, ON to Halifax, NS with fuel left in the tanks. Or we could hit every island in the Bahamas. The entire Great Loop could be done with only four gas stops. And while I'd rather not have jerry cans on board, each one (25 L) would add about 150 miles if we were to bring them.
Alternatively, we could use that tank capacity (plus a few shots of stabilizer) to hedge against Canada's notoriously volatile fuel prices. Or we could punch the throttle, cutting the range to 250-500 miles, which is an entire summer's worth of weekends at the local beach. It's nice to have options.