Model Tank Experiments by Benjamin Franklin
By Captain Elliot Snow (CC), U.S. Navy
It is not generally known to naval architects and marine engineers that Benjamin Franklin, at one time, interested him. self in the subject of the resistance of ships and that he actually made some experiments with a model to determine the difference in resistance of barges between shoal and deep water navigation.
His interest in this subject and the experiments which followed arose from a chance inquiry that he made of a boatman while traveling on one of the barges in a Holland canal. The results of these experiments are recorded in a letter written by Dr. Franklin, dated Craven St., London, May 10, 1768. This letter is of so great historic interest, that it is here quoted in full:
"To Dr. John Pringle, London.
On the Difference of Navigation in shoal and deep water.
Craven Street, May 10, 1768.
Sir:
You may remember, that when we were traveling together· in Holland, you remarked, that the trackschuyt in one of the stages was slower than usual, and enquired of the boatman what might be the reason; who answered that it had been a dry season, and the water in the canal was low. On being again asked if it was so low as that the boat touched the muddy bottom; he said, "No, not so low as that, but so low as to make it harder for the horse to draw the boat." We neither of us at first could conceive that if there was water enough for the boat to swim clear of the bottom, its being deeper would make any difference; but as the man affirmed it seriously, as a thing well known among them; and as the punctuality required in their stages was likely to make such difference, if any there were, more readily observed by them than by other watermen who did not pass so regularly and constantly backwards' and forwards in the same track, I began to apprehend there might be something in it, and attempted to account for it from this consideration, that the boat in proceeding along the canal, must in every boat's length of her course, move out of her way a body of water, equal in bulk to the room her bottom took up in the water; that the water so moved must pass on each side of her and under her bottom to get behind her; that if the passage under her bottom was straitened by the shallows, more of that water must pass by her sides, and with a swifter motion, which would retard her, as moving the contrary way; or that the water becoming lower behind the boat than before, she was pressed back by the weight of its difference in height, and her motion retarded by having that weight constantly to overcome. But as it is often lost time to attempt accounting for uncertain facts, I determined to make in experiment of this when I should have convenient time and opportunity.
After our return to England, as often as I happened to be on the Thames, I enquired of our watermen whether they were sensible of any difference in rowing over shallow or deep water. I found them all agreeing in the fact, that there was a very great difference, but they differed widely in expressing the quantity of the difference; some supposing it was equal to a mile in six, others to a mile in three, &c. As I did not recollect to have met with any mention of this matter in our philosophical books, and conceiving that if the difference should really be great, it might be an object of consideration in the many projects now on foot for digging new navigable canals in this island. I lately put my design of making the experiment in execution, in the following manner:
I provided a trough of plained boards fourteen feet long, six inches wide and six inches deep, in the clear, filled with water within half an inch of the edge, to represent a canal. I had a loose board of nearly the same length and breadth, that being put into the water, might be sunk to any depth, and fixed by little wedges where I would chuse to have it stay, in order to make different depths of water, leaving the surface at the same height with regard to the sides of the trough. I had a little boat in form of a lighter or boat of burthen, six inches long, two inches and a quarter wide, and one inch and a quarter deep. When swimming, it drew one inch water. To give motion to the boat, I fixed one end of a long silk thread to its bow, just even with the water's edge, the other end passed over a well-made brass pully, of about an inch diameter, turning freely on a small axis; and a shilling was the weight. Then placing the boat at one end of the trough, the weight would draw it through the water to the other.
Not having a watch that shows seconds, in order to measure the time taken up by the boat in passing from end to end, I counted as fast as I could count to ten repeatedly, keeping an account of the number of tens on my fingers. And as much as possible to correct any little inequalities in my counting, I repeated the experiment a number of times at each depth of water, that I might take the medium. And the following are the results.
Water 1½ inches deep. 2 inches. 4½ inches.
1st exp. 100 94 79
2 104 93 78
3 104 91 77
4 100 97 79
5 100 88 79
6 99 86 80
7 100 90 79
8 100 88 81
813 717 632
Medium 101 Medium 89 Medium 79
I made many other experiments, but the above are those in which I was most exact; and they serve sufficiently to show that he difference is considerable. Between the deepest and shallowest it appears to be somewhat more than one fifth. So that supposing large canals and boats and depths of water to bear the same proportions, and that four men or horses would draw a boat in deep water four leagues in four hours, it would require five to draw the same boat in the same time as far in shallow water; or four would require five hours.
Whether this difference is of consequence enough to justify a greater expense in deepening canals, is a matter of calculation, which our ingenious engineers in that way will readily determine.
I am, &c.,
B. Franklin."
The principal factors which differentiate shallow water resistance from deep water resistance are now fairly well known. These shallow water effects are pointed out in most of the treatises on the resistance of ships, and screw propulsion. A very simple explanation of this kind is to be found in the Speed and Power of Ships, by Rear Admiral D. W. Taylor (CC), U. S. N., Retired, from which the following extracts were taken:
“When the water can move freely past the ship in three dimensions, the pressures set up by the ship's motion would naturally be less than when shallowness compels the water to motions approaching the two dimensional characters.
In shallow water these extra pressures cause waves larger than those in deep water, and in shallow water the lengths of waves accompanying a ship at a given speed are greater than for the same speed in deep water. These are the principal factors differentiating shallow water resistance from deep water resistance. There is a third factor; namely, the change in stream velocities past the surface of the ship when in shallow water. This factor would increase resistance somewhat, but its effect would seem to be so small that it is not necessary to consider it since we cannot at present determine with much accuracy the effect of the dominating factor; namely, the change in wave production.”
It is also interesting to note, in connection with Benjamin Franklin's historical experiment, that the question of increased resistance in canal navigation had to be taken into account when designing the electric locomotive tractors used at the Panama Canal.