It's Not Very Complicated...Just Get In The Boat And Row
Think rowing is a relatively simple sport? Think again. (The following article on balance is copied from www.btinternet.com/~furnivall.sc/)
In this article the classic analysis of the static stability of ships is extended in a way that seems to offer some useful insights to rowers in racing boats. The investigation started out as simple curiosity to see what happened when I plugged some numbers for racing boats into standard fluid mechanics theory. The results were unexpected, hence this article.
Balance does not get much of a mention in rowing literature. Generally textbooks seem to assume that if everything is kept symmetrical then balance will emerge naturally. The older texts contain the unemphasised assumption that beginners will always start out in wide stable boats and graduate through a progression of finer craft. I suppose coaches did not need to worry about it much in those days as the boatman would normally issue the appropriate kit. This approach has continued, some modern texts, such as the ARA Instructors Handbook, suggest starting off beginner scullers paddling square blades without really discussing what sort of boat is required to do it.
I suspect that it is relatively common in clubs today for beginners to be put into fine hand-me-down boats at a relatively early stage, which perhaps makes balance more of an issue than it used to be.
The article is in two parts: Part 1 follows the investigation in detail. Part 2 contains conclusions and a Q&A section. The less technically minded might want to skip Part 1 and go straight to Part 2, but I would recommend that if you are going to use this material you should read Part 1 to understand the reasoning and its limits.
Racing rowing boats are members of the class of vessels where the centre of gravity (CofG) is some distance above the centre of buoyancy (CofB) of the hull. This type of ship is stable provided that the CofB moves sideways faster than the CofG as the ship rolls, a condition that is satisfied if the CofG of the ship is below a geometric point known as the metacentre (MC). The MC is basically the point through which the CofB acts for small amounts of roll. If the CofG is over the MC then the ship will roll over at the slightest disturbance. See any textbook on basic fluid mechanics for a full explanation of these concepts, the derivation of the limiting equation and formal definitions of stability and balance (equilibrium).
Figure 1. Metacentric stability.
The equation defining the limit of stability of ships is:
BG=V / I
BG = Metacentric height, the limiting distance of the CofG of the ship over its CofB.
V = Volume of fluid displaced.
I = 2nd moment of the horizontal waterline shape about the axis of rotation of the ship.
Points to note about "metacentric stability":
Measuring up some boats in the Furnivall Sculling Club boathouse and plugging in the numbers we get the table below. None of these numbers are very exact, but they serve their purpose (in particular the method used to approximate the MC is optimistic rather than pessimistic). All dimensions in cm. Crews on board unless stated otherwise. CofG etc. are referred to the waterline to allow easy comparison between different boats.
|Single scull||Eight||Mondego||Empty scull|
|Max. hull waterline width||27||57||74||18|
|Max. submerged cross sectional area (cm^2)||220||770||730||38|
|CofB below waterline||4.5||7.4||5.3||1.1|
|BG (MC over CofB)||7.7||20||47||13|
|Metacentre (MC) over waterline||3.2||13||42||12|
|CofG over waterline
|Seat height over waterline||11||9||11||N/A|
Table 1. Sample boat data.
Hum, not what was expected. Note that in both loaded racing boats the CofG is well over the MC, indicating that the boats are unstable. The Mondego on the other hand has the CofG well below the MC making it statically stable. Mondegos are known to be easy to scull with the blades off the water, even by beginners. The eight measured is considered a straightforward boat to sit for normal club crews.
The case of the empty scull makes sense as a check on the method, given that the MC is likely to be an overestimate. This particular boat will sit flat when empty, but if I add a PaceCoach to a bracket over the feet it will then fall over to either side, it has lost stability. The unloaded CofG is that close to the unloaded MC.
So where does that leave us?
Following the odd result for racing boats I plugged in some numbers for a punt as an example of a wide flat boat with a high CofG. I found that the MC was still only 60cm or so above the waterline. The CofG of a human is about 100cm up from the feet. Even a with heavy punt that makes combined CofG of about 80cm+ above the water line with the punter standing on the deck (Cambridge style). How is it possible to pole one of these things without capsizing?
The answer seems to be that we are not dealing with a rigid system.
As I recollect when you first try to stand up in a punt you generally get a load of wild oscillations, which usually go away as you learn to relax and let the boat move freely under your feet. The boat hull now balances. What I think has happened from a mechanical point of view is that the boat sees your weight acting somewhere between your feet but exerting no turning moments, i.e. as far as the hull is concerned your weight is at deck level, which is well below the MC. So the hull is happy. You maintain your balance on top of the hull by VERY gentle differential pressure on your feet (there is some stability reserve) and by using the pressure of the pole against the water and river bottom, i.e. by using a load path external to the hull to help manipulate your mass.
The critical points about "punt stability" are:
Looking again at Table 1 we see that the MC for the eight falls just above seat height. So if you can sit without disturbing the hull in any way, the hull might be stable (just!). Sharing your weight between your feet and your backside will lower your apparent weight in the boat which helps to improve things. More stable eight designs could well get the MC higher up.
Looking at some example cases for racing boats where the MC is just above the seat and ignoring the weight of the boat:
Figure 2. "Punt Stability", a system with one degree of freedom.
CASE 1. Everything is vertical. If the crew is rigid in the boat, the system is unstably balanced, i.e. it will fall over if disturbed in any way. If the crew is flexible, the hull has a chance to "sit" properly.
CASE 2. Rigid crew off vertical. Classic ship analysis, roll over time.
CASE 3. Boat tilted but crew vertical. From the crew's point of view they are leaning out of the boat. If the crew sits rigidly this is the same as case 1 with an unflat hull. If the crew is flexible the hull is stable, but will remain tilted over. Look or feel familiar? If the MC is lower in the boat the CofB will act along the dotted line and we still have case 2.
CASE 4. Boat tilted and crew leaning further over. With a high MC the boat will now tend to fall back if the crews sits rigidly (at last!). With a lower MC the CofB acts along the dotted line and we have case 3 again, the hull is not flat and the crew is hanging out, but the situation is in equilibrium.
Although crews go on about boats not being "balanced", in fact they usually do have the blades off the water most of the time. This implies that the combined CofG is roughly over the CofB, i.e. we have case 3. In other words the boat is balanced in the sense that forces are more or less in equilibrium, but it is not flat, one rigger is up and may stay up.
"Punt stability" seems to be an improved explanation in that it provides some insights that match common experience:
At this point a digression to see how various geometric shapes look in the light of static stability and punt stability. Considering various parallel sections corresponding to the middle of a four or eight:
|CofB below waterline||7.44||9.35||6.95||8||10.3||7.82||9.6|
|BG (MC over CofB)||19.8||9.35||18.5||12.1||13.5||21.9||12.1|
|Metacentre (MC) over waterline||12.4||0||11.6||4.1||3.2||14.1||2.5|
|Metacentre over seat||3.2||-10||1.6||-6||-7||4.1||-7.5|
|Surface area (cmˆ2)||9490||9026||10842||10400||10322||9558||9313|
|Surface area (% of semi-circle)||105||100||120||115||114||106||103|
Table 2. Sample section data for sections of 770 sqcm
Notes on hull shapes:
It is a common experience that moving boats are generally easier to sit flat than static ones. This suggests that there can be significant dynamic self righting forces acting on the hull.
Such a consideration would be not very meaningful in the case of ships as the relative size of dynamic forces to static forces are small and adequate stability when stationary (e.g. when loading) is vital. This is perhaps why this type of analysis tends not to appear in the ship stability sections of fluid mechanics textbooks. In the case of racing boats the opposite is true: we do not really care if they are unstable at rest (as they can be satisfactorily controlled by the oars resting on the water), just so long as we can keep them near enough flat when in motion. Racing boats are sufficiently light and responsive that small dynamic forces can have an appreciable effect.
Consider the eight in Table 1 travelling at 5m/s (1:40 split). With a frontal area of 0.077sqm this gives approx. 400 kg of water displaced a second (or about a ton a stroke...). Admittedly most of the water flow is pulled out of the way by the standing wave system, but it will give rise to significant forces caused by momentum change of the order 100's of N normal to the skin of the hull. In particular the flat V shape of the bottom between the bows and the shoulders will produce righting moments in much the same way that they do in motor boats at speed. See figure 3. These forces are in addition to the static buoyancy righting effects considered above.
Figure 3. Self-righting forces on V section moving hull.
I suspect that other features of the hull shape such as camber and flat bottoms have similar effects, especially when the boat is at speed with the bows up and hull slightly inclined to the flow of water.
Points about dynamic stability:
The oars in the gates are the other point of contact between the rower and the hull.
The weight of the oars is carried out on the riggers which gives them a large lever to work on the hull. The oars are waggled up and down each stroke which produces significant transient forces up and down on the riggers. Any out of balance motion between the actions of the oars on each side will tend to roll the hull.
There is a twist to do with changes in hand heights. If one side is up and the rowers on that side lift their hands, then they will temporarily reduce the vertical load down on the rigger and thus tend to make the hull roll up further. Similarly if the other side drop their hands, they will tend to push the riggers down. Even if the crew does not lift or drop their hands during the recovery when the boat is not flat, they will have to do so at the catch in order to reach the water, giving that nasty extra little lurch just before the catch. This is a positive feedback situation. Always unhelpful in dynamic systems.
The oars also allow the rower to exert vertical forces on the water independent of the hull, via the pitch in the blades and perhaps other factors. When the oars are in the water you can force the hull flat and correct your body position ready for the next stroke.
Points about oars and hand heights:
The practice of recovering your blades by dragging them lightly along the water surface is known by various names. It is mainly associated with singles and pairs, especially in the early stages of learning to scull. It is obvious that if you drag one blade along the water lightly some of the weight is taken by the spoon and it will reduce the weight acting down on the rigger. Hence that side of the hull will tend to come up. If you lift your hand further you can actively push down on the water. By exact hand control you can scull a boat dead flat this way.
During the recovery if the blades are off the water you will get a small aerodynamic lift force acting on the spoon due to the angle of attack of the spoon on the feather. If the spoon is very close to the water you seem to get a "ground effect" enhanced lift similar to that experienced by aircraft operating very close to the ground. The closer you get to the water the greater the lift and that side of the boat tends to rise, a nice negative feedback system that gives a reduced version of skimming along the water without actually having to touch the surface.
I think that this is why it is easier to scull neatly on dead flat water with a light head breeze. You can keep the blades off the water, or touch only briefly occasionally, and still get assistance from the unweighting of the riggers to make the boat conform to your hand heights. I suspect that waves break up the "ground effect" and force you to recover higher anyway. Paddling with square blades cuts off this assistance completely which I think is why it is such a pain in singles. It may also explain why scullers are reluctant to square very early.
Is seems to me as a general observation that the smaller the boat, the closer to the water the rowers recover their blades. This seems to me to be evidence that this is a significant effect. I don't think that it is just nervousness or laziness, I think it is done because it makes the boat easier to control.
Note that crew boats require you to get the spoons right off the water to clear the puddles coming down from rowers behind you, hence this strategy is not available. Which may be why crew boats have to be built with more basic stability to compensate.
Points about skimming the water on the recovery:
OK, so how can you balance a single in choppy water if you can't skim the water, the boat has no static stability at all and there does not appear to be any dynamic self-righting effects? The answer as I see it is that you don't balance it as such. What you do is hold it approximately flat during the recovery, that is all that is necessary. The more skilled you are the better the approximation.
Basically if you set the boat up at the finish and swing straight down the hull, your upper torso is not going anywhere very quickly and its inertia can be used as a reference point to sit the boat flat by controlling the hips, feet and hands. The low rolling resistance of sculls means that you do not have to do much to achieve flatness.
This is a bit like walking, the system is not truly balanced, it is a series of controlled falls. The key point is that the sculler has reference to the water during the drive to control the body in preparation for the next recovery.
Points about body inertia control:
Summarising the above into a hierarchy we get Table 3. Depending on the level of stability offered by the boat, different control techniques can be used to keep the boat flat. I suspect that beginners in crew boats might tend to learn these skills more or less in the sequence shown in the table. Scullers would do it differently (don't they always?).
|Affected by oars||yes||yes||yes|
Table 3. Hierarchy of control techniques workable in different boat types.
Points to note:
To summarise the main conclusions from Part 1 in no particular order:
Some of the above may be news to some people, I make no apologies if they are all obvious. Checking around among members of Furnivall Sculling Club during the preparation of this article it became apparent that people have quite widely different ideas about whether boats are stable or not, what causes it, how to balance boats in practice and whether all boats work the same or not.
As far as I can see the classic coaching points that most people trot out are unchanged by this analysis, but the reasons behind them and how they might be presented to a crew may be affected.
Suggestions might include:
They are the product of evolution. It was found that finer boats went faster. As they got thinner the best rowers or scullers could still learn to control them, just. The first formal analysis of ship stability was done in the 1870's by Mr Froude (he of the Froude number) for the Royal Navy after some new battleships turned over unexpectedly. The outrigged shell was developed in the 1840's and 50's, they didn't know it couldn't be done, so they did it!
If you consider that the reaction time to produce a large action in response to unexpected events is of the order of a second or so then it is hard to see how reactive type control alone looks after flatness during a recovery that lasts around a second at racing speeds. I think that flatness needs to be asserted via some combination of hull stability and technique.
Of course the crew have to (try and) fix any major disturbances in the boat as they arise.
If you look at eights that flop over when going through launch washes, it seems to me that often it is more the crews reaction to the wash that causes the boat to flop, rather than the impact of the wash itself. The counter-intuitive nature of the beast bites back, which to me does not auger well for the idea of reactive control.
Not so in racing boats. They are not stable. If the boat is exactly upright and the crew exactly symmetrical that is not enough to ensure that the situation continues. The slightest disturbance (the proverbial butterfly landing on a rigger) will cause the boat to inevitably fall over. You then have to correct the imbalance and return it to the symmetrical position, in other words you still have to be able to "sit" the boat. On the other hand a basically symmetrical crew will do less to upset the boat, making the job much easier. In statically stable beginner boats simple symmetry is enough, the boat does the rest.
To press hard on a rigger usually means that you lean slightly out to that side to apply the force. The static analysis above shows that for racing boats consistent leaning will simply exacerbate a consistent lack of flatness. If a boat has lurched over for some reason you can force it back towards flat by leaning over then tweaking your hips. If this lurch happens all the time then doing the tweak all the time is just papering over the problem, the problem is why it goes off flat in the first place.
Gentle pressure against the rigger does allows the rower to control their upper body laterally relative to the boat and stop the rower flopping around which can be a problem in itself. In particular lateral pressure does tend to reduce leaning away from the rigger at the finish. In either case suggesting pressure on the rigger may help a lack of flatness problem. Note also that stable training boats do respond as expected to leaning.
Bigger fins will damp the rolling of the hull slightly, but they will not correct any loss of balance or flatness. Likewise I don't think full length keels help balance as such, but they are associated with wider more stable boats.
Some rowers need some sort of reasonable explanation to help the learning process. Too many engineers, accountants, medics and computer programmers I suppose. I know it helps me. If you find it useful, fine. If you "just do it", then I am surprised that you have read this far.
Balance seems to me to be one of the black magic areas, I have not come across any complete or compelling explanation either verbally or in the literature. I have heard explanations of balance and how to achieve it which are plain wrong which can serve as a block to effective learning. I have also seen coaches and coxes asking crews to do what I now believe to be the impossible, this is likely to produce frustration and loss of confidence. Perhaps this analysis may help.
You don't. Nor do I for that matter. Please take all the above with a pinch of salt. Test it to see if it seems right to you before taking it for granted. Time will tell.
Even if the above analysis turns out to be correct, there are no magic solutions. You still need to learn to "sit" the boat properly. At best I hope to make the learning process a little shorter and clearer.
Good for you.
To most people the term "balanced" means to be in stable equilibrium. This is the sense that I have generally used in this article. However it also has the sense of something being actively held in place, which is perhaps closer to the mark for rowing. I suspect that some rowers get confused a little by the terminology because they are expecting a balance (passive static equilibrium) that will never happen in most racing boats. It also happens that a boat can look flat and steady enough from the outside but feel twitchy from the inside so the coach thinks it is balanced, but the crew do not.
I think possibly so. Certainly the clinker eights I learnt to row in were more stable than current plastic boats. As far as fine shells go two tangible bits of evidence I have come across recently support this idea. The cross section for the winning Oxford blue boat of 1901 shown in G.C.Bourne's "A Textbook of Oarsmanship" looks very broad and flat bottomed by today's standards. Remember that this was not too far off the era when successful Oxbridge crews might go to the Olympics. Recently we had a clear out of old wooden shells from the rafters of the Furnivall Sculling Club boathouse. Many of these boats would again be considered quite flat bottomed and broad by modern standards.
It might be that in days when eights were made by local builders, in practice the designs offered would tend to favour user-friendliness. Builders would not want to cultivate a reputation for making boats that lived on racks. Nowadays boats are moulded rather than built in the round and there is the temptation is to buy boats that come from the same mould as world championship winners.
Obviously if you have no choice about your boat you can get beginners going by doing a lot of paddling bow four/stern four. However this does result in less effective use of water time and cold crews.
As I see it balance on a high wire is different to a racing boat so the analogy is suspect. High wire artists ultimately maintain balance by moving their feet from side to side. The pole simply slows up the counter rotation of the upper body. (High wire artists please feel free to correct me on this.) If you watch a wire walker without a pole there seems to be a lot of arm waggling to produce the same effect. Boats do not allow you to move your backside sideways. Oars do act as balance poles in that they have a lot of rotational inertia and can produce relatively large forces at the rigger for little motion, which may be the point of the analogy. As noted above waggling oars around is liable to produce positive feedback, which is not a good idea to encourage.
Pass. Personally I prefer ultra-lights for sculling, but I think that this is because my hand control is a bit erratic so lighter blades reduce the disturbing impulses on the hull as I thrash around. If you have good hand control, heavier blades will increase the resistance of the hull to rolling, which might help you in rougher water and make the hull feel firmer.
In addition to the obvious wave impacts on the side of the hull, I think that the circular currents making up big waves will produce uneven self-righting forces on the hull. I suspect that in really poor conditions any dynamic self-righting properties of the hull can be swamped out altogether. Obviously the bigger the boat the worse things have to get to upset the hull.
Note also that twitches in the hull, especially in singles, can lead to over control by the rower introducing further problems. Personally I have trouble with this one: trying to relax helps, but I have found no simple answer.
And that's just balancing the boat! Why don't you check out the US rules of racing if you still don't think that rowing is a complicated sport. Or perhaps you may want to check out the physics of rowing.