No long distance surface swimming animal exists because this is not energy efficient. Even whales that need surface for breathing (because they started as a surface animal similar to a nutria -ambulocetus-) swim now below surface - why ? because they cruise up to 12,000 miles each year and nature shapes all animals to be energy efficient. Here we are - if you are looking for a model for a energy efficient ocean crossing submarine yacht take this. A 200 ton whale with a length of 30m (cut some of the tail section for hydrodynamic efficient length - take some 25m) can come up to a speed of 30 knots and has been measured at those speeds. Biologists and Physiologists estimate its maximum power output at 400 horsepower. Whales are mammals so their energy physiology is similar to other mammals. Which means there is a big gap between the energy output you can get from the organism in a emergency situation for a few minutes of fast swim and the energy output you can get 24 hours a day. The most educated guess on that is a factor 10 you can run very fast for 1 minute but if you wander 24 hours a day you have to do it at a slower rithm. This means what you have on a whale tail 24 hours a day during wandering is maybe 40 horsepower possibly less. If you take into account that whales do not feed which means do not re-fuel 6-8 months during wandering - how is this possible ? - only if they use VERY VERY little energy for swimming over VERY VERY long distances. What is the efficient speed range ? Smaller whales cruise at some 3 knots bigger whales at up to 6 knots. Taking a stream speed of 3 knots in your favor as ben franklin did in its 30 day Golf Stream drift dive - you could have a whale economic ocean crossing at 9knots over ground in a submarine yacht - not bad ! Having this in mind i took my prototype concrete submarine to water back in 1996 it was whale shaped had 20 tons like a small whale and my most important question was not top speed with a big engine - this is quite clear anyhow - my question was the limbo - how low can you go… so what i did first was installing a ridiculously small electric engine of 200W into the sub and pushed the switch. - What happened? First nothing then after a couple of seconds the hull took up speed and kept taking up speed until it reached a speed of what would be in the range of a whale efficient cruising speed - some 3 knots. So i never came to the point to install the big combustion engine i had in mind in first place - it was not necessary. I later put a small generator in to reload the small battery pack and extend the range - that was all. In all my submarine yachting years i never saw a situation i would have had a need for a bigger engine. This ridiculously small engine pushed me trough storms had no problem to get nose into the wind… So i am well aware what engine size is recommended for surface yachts - BUT - based on my own experience i would be concerned that such a engine would have a short life in a yacht submarine yacht because it has to run all the time in under load during cruising . I also have no problem if somebody wants a 400hp engine in a 200 ton submarine yacht to run all the time at whale emergency speed of 30 knots - you could water ski behind it…
My personal preference is doing it like those gentle giants - cruise oceans energy efficient at moderate speed.
When you plan an engine for a submarine yacht you should forget anything that is recommended for surface yachts and come back to the basics. Fortunately there exists a fine model made by mother nature that has about the size of a submarine yacht and travels long distance as a submarine yacht is supposed to do - Whales! A streamlined body such as a whale can travel over long distances with incredibly low energy use. Studies suggest that a whale uses 5 times less energy for swimming under surface than swimming on surface where additional drag from wave resistance comes up. A graywhale of 18 tons displacement has 3000 kg (14 kg of fuel/day) to travel 20.000km (95km/day) in this journey he has about 589g/hour of fuel available for life support and locomotion. To simulate the locomotion model of gray whale a submarine yacht of the size of my prototype (20tons) is well equipped with a diesel of 1-3 horsepower. This fits well with my own field data that suggest that a small electric engine of just 200W can move a submarine yacht hull of 20 tons under all weather conditions. Such a submarine yacht is able to go 95km per day with 14kg fuel use per day - the problem is you might not find a diesel small enough for this.
…right whales are slow swimmers, rarely exceeding 5 knots, with an average speed of only 2 knots. Gray whales are also not too fast, clocking a maximum speed of only 6.5 knots. Humpback whales do about 5 knots on average, but can put on bursts of 9-10 knots. Sperm whales are much faster, doing about 10 knots on average, and able to accelerate up to 20 knots or so if pushed, though only able to maintain this speed for a short period. Speeds of 14 -18 knots have been reported for the minke whale. The sei whale appears to be the fastest of the lot, able to achieve a sprint of about 32 knots, although again for only a short stretch. Some dolphin species can also go this fast, and are generally a lot faster than whales on average.
hydrodynamic cost of swimming for a graywhale
muscle and digestive efficiencies of 25% (Gosline 1993) and 80% (Thomson and Martin 1986)
Models developed by (Bose and Lien 1989) for a fin whale
model for a typical gray whale (Sumich 1983) estimates the daily requirements for gray whale locomotion come close to 60 Mcal/day.
Gray whale if swimming near to surface encounter wave drag which can increase total drag by a factor of five (Hertel 1966)
It makes sense for whales to travel at depth greater than 3 times their body depth (Sumich 1983)
Metabolic rate from oxygen consumption Studies:
(sumich 1983, Wuersig et a. 1986, Wahrenbrock et.al.1974, Highsmith and Coyle 1992)
Bose and Lien 1989, Hui 1987,
Bose N, Lien J (1989) Propulsion of a fin whale (Balaenoperta physalus): Why de fin whale is a fast swimmer. Proc R Soc Lond B 237:175-200
Hertel H (1966) Structure, form and movement. Reinhold Publishing Corporation, New York.
Hui CA (1987) Power and speed of swimming dolphins. J Mamm 68: 126-132
Kleiber M (1975) The fire of life: An introduction to animal energetics. Robert E Krieger Publ Co., Huntington, New York.
Pike GC (1962) Migration and feeding of the gray whale (Eschrichtius robustus). J Fish Res Bd Canada 19: 815-838
Sumich Jl (1983) Swimming velocities, breathing patterns, and estimated costs of locomotion in migrating gray whales, Eschrichtius robustus. Can J Zool 61:647-652
Wahrenbrock EA, Marushak GF, Elsner R, Kenney DW(1974) Respiration and metabolism in two baleen whale calves. Mar Fish Rev 36:3-9
Blix, A.S. and Folkow, L.P.(1995) Daily energy expenditure in free living minke whales. Acta physiol. scand. 153, 61-66
Hui (1987) estimated that dolphins energy bursts represent a 166-fold increase of the metabolism over resting rates.
Migrating gray whales have a minimum CT (cost of transportation) that occurs at the mean velocity of 2.0m/s (Sumich, 1983). The stored engery resevers allow a migration of 15.000-20.000km during which the whales fast.
Cost of locomotion estimated, based on Lockyer(1981) and an average swimming speed of 6.3km/h for gray whales (Perryman et al. 1999)
Total blubbermass used in migration in a 18000kg whale is 3000 kg available for six to seven months without feeding - while migrating 20.000 km
energy by respiration…
The estimated O2 consumption of about 150 l.min(-1) is in line with the general allometric regression for mammals and corresponds to an energetic expenditure of 85-95 kJ.kg(-1).day(-1).
( BLIX AS, FOLKOW LP. Acta Physiol Scand 1995;153(1):61-6.) Mink Whales
…We found that cost of swimming is remarkably low in these large animals and that their estimated daily energy expenditure on average only amounts to 80 kJ kg-1 day-1.