Hi I hope that one of you fluid dynamics people can answer this - I am NOT expert in this field. I race sailing yachts and it is a well known tactic for smaller boats to get close to bigger boats so that they can sit on the stern wave of the bigger boat. As a result the small boat can surf, leading to rapid acceleration. My question is, does the small boat slow down the big boat when it does this, even if the effect is very minimal? Or does the small boat use "the waste energy" of the big boat and therefore have no impact on the big boat's speed?

In my opinion, it does slow down the big boat inversely proposional to distance(not necessarily linear). For the limiting case, the smaller boat is getting closer to the big one and eventually tied together, then it is one bigger boat, surely it consumes bigger energy.

Junseok

If I tie the boats together with a rope, it won't matter how far apart they are - the small boat will slow down the big boat (assuming the big boat is going faster in the first place due to its greater water line length). In the scenario I described, are the two boats not just "tied" but instead of using a rope, they are connected by the wave?

Hi, Let us assume that the big boat has gone couple of miles ahead and now there are some waves left behind which the small boats can use. So i guess there is some waste energy which is being used. So probably it depends where the small boat is placed. Although Kim's answer indeed makes a lot more sense. -amol

I believe the small one can influence the big with changing flow condition around the hull. How much it will be? Let us make a computation...

The small boat is surfing the wave in the wake of the large boat, effectively using a component of gravity to help propell it. As to the small boat slowing the larger boat then if they are sailing boats this will depend upon the sailing psition relative to the wind is running or reaching. The small boat may steal the large boats wind. The effect under the water may be different. Is the drag of the large boat increased by the presence of the smaller boat ? this I'm not sure ! What happens in motor racing, where the one car gets a tow from another. Is the lead car impacted, or is it just a benefit in drag reduction to the trailing car ? I'd assume the same principle may possibly apply ?

Has something basic been ignored? The small boat can get up on a plane, but usually larger boats can't. They are limited by their theorectical hull speed, which is about 1.14* sqrt(length at waterline). That is because the large boat's speed is set by the one standing wave length.

I'm not sure that the right questions are being asked here. It seems to me that this is quite a complicated question, and I doubt that a simple energy argument is going to give an accurate statement of the dynamics.

I know that in low Reynolds number flows (Stokes flows / viscous flows) there are numerous theoretical results relating to the motion of aligned bodies. (For example, two spheres together fall faster than when separated). In the wakes behind watercraft such as those in discussion, however, we're certainly dealing with a very high Reynolds number flow (turbulent).

I think this is classic aerodynamics, which I know very little about, but could someone explain why bike racers (say, in the Tour de France) align themselves to increase the group speed? (bad terminology, sorry) I think there are some surprising effects, like the leader's speed *increases* with the number of bikes trailing...

Should similar effects apply here? Or are they negligible?

The wave propogation speed depends on pressure near to propeller and the pressure at downstream (main stream). The boat adds resistance to the wave propagation, and hence increase the back pressure just outide the propeller, which means an additional work on the impeller in propogating the wave.

Its a sailboat - if they have propellers at all they are either folded or out of the water! I sail. The lead bigger boat does not get slowed down by a smaller boat surfing on its stern wave except of course (as someone else mentioned) if the wind is aft and the smaller boat steals some of it. A big stern wave is wasted energy as far as the big boat is concerned, but the small boat is able to extract some of that waste energy to move faster.

I guess, at some point of time, we might have studied that when a train passes by, it kind of attracts things towards it. The reason being the "temporary" vacuum being created there which has to be filled up by the surrouding air. When this air moves, it tries to take along anything which it can to fill up that space.

Something similar should happen in case of sailboats too. The bigger sailboat would create a "temporary" vaccum not only in air but also in water (due to it's hull), thereby trying to pull whatever it can, to fill up the space. This is far more significant than in the case of a train since now you have an additional force of water. (I would say smaller boat would also attract the bigger one but that force would be much lesser)

Naturally, with the approach of another piece (forget the smaller boat but let's say anything), all the smooth hull calculations for the sailboat go for a toss. Understand it this way that you have a lump attached to your big sailboat at some distance. This might cause quite a drag to the big sailboat.

So, the bigger sailboat is definitely going to slow down. Since every action has a reaction, naturally, the smaller boat is going to go faster until both boats go with the same speed.

There is lot of maths to it than just the plain simple words. I worked on sailboat CFD designs for quite sometime and still get perplexed at times In any case CFD, with wake and turbulence is never that easy.

As for the bicycle question which Saverio asked, it's a little simpler. Anything would move faster if it has a nice conical kind of a shape towards it's back. By having more cycles at the back, the leader is able to reduce the drag for him, hence might go faster. Someone might say, hey, the last cyclist would have the big drag!! With the long chain of cycles, the process of air detachment goes quite slower hence the drag for the last cyclist should be lesser than the drag for just one cyclist going alone. And in any case, he is the slowest chap

The physics are quite simple. Large boat wastes some energy making a wave. Small boat extracts some energy from that wave to go faster.

Assuming we are not in a canal or in very shallow water, the amount of energy wasted making waves is strictly a function of the big boats hull speed and hull shape. No effect on energy required by what happens to the wave after it is generated.

Thus big boat is NOT effected by presence of small boat surfing on its wake.

As the person who started this debate (apologies!), let me throw my thoughts into the melting pot.

I agree that the large boat wastes energy by creating a wave. I also agree that the small boat can harness some of the energy from that wave, just as it would harness the energy from a "natural" wave. So maybe the question is, does the presence of the small boat just behind the big boat cause the big boat to waste MORE energy than it would have if the small boat had not been there?

If I put the problem another way, suppose there were 50 small boats all riding the stern wave and all going faster than they could otherwise go as a result, are we saying that the big boat would still not be slowed down, despite "towing" all these small boats?

My intuition tells me that 50 small boats would slow the big boat, but I cannot figure out the science.

Hi! Interesting! I've some experience cycling but not boating. In cycling, I could feel the drag changes as I change my position behind a rider/bicycle. Depending on speed, the position for maximum benefit of drafting changes. This change is associated with the exact behavior of the turbulence wake behind the first rider. We can't see the wake behavior but we can feel the aerodynamic drag. For boats, I think some adjustments have to be made ad hoc for you to fully take advantage of drafting or surfing the stern wave.

At one position of the small boat, both may go faster as both boats now comprise of a hydronamically efficient entity depending on the boat speed. At another position, the small boat may alter the wake behavior such that for the leading big boat it generates more parasitic hydrodynamic losses. In this situation both boats may be slowed down as the extra parasitic losses caused the big boat to slow down while some lateral forces and other forces may be generated on the small boat giving it a rough ride.

This is perhaps an over-generalized speculation of mine based on some experience. Anyway, if I were to double-team against your boat, I'd send a small boat to sit in your stern wave and carefully adjust itself in a parasitic manner so that it will change the behavior of your wake thereby slowing both its speed and yours while I sail my boat towards the finish line.