# Dynamics - The Trim Equation

Hi Kevin,

Wups! Yep force is vector - brainfart there. F=MA, p=mv - both vectors Sorry mate. I suppose the general connotation in the physics papers I read/study somehow infers that with F vector is less of a concern and with p it’s intrinsic.

Sorry about that… Stand by my other items, tho.

Cheers!

Kevin,

I’m not sure how you are able to conclude water moving across the surface of a surfboard results in a propulsive force. This is not suggested by the Savitsky paper you reference. Water moving across the board’s surface will result in dynamic lift, which may have a down-the-wave component depending on trim. My guess is the down-the-wave component is of much lower magnitude than the drag component that also results from water moving across the board’s surface. That being the case, the “force” can be reduced to a normal component and a drag component. This is consistent with Savitsky’s treatment. There is no “propulsive” force in Savitsky’s paper (Savitsky calls it a resistance force).

A real life example is the artificial wave at the Wavehouse. Water moves across the surface of the board, yet the board and rider stay in the same location. No propulsive force due to water moving across the board’s surface in that case.

You assume Pz = W. That’s fine as long as the force P includes all the forces acting on the board except gravity, i.e. drag and bouyancy. It’s also fine if you are assuming the board is in equilibrium. Assuming your math is correct (I didn’t check), you conclude the resultant force is a function of W (weight) and trim angle only and nothing else matters. What happened to the “propulsive” force?

Paul

I refer you to the ‘Dynamics - Surfing the force’ thread.

Breifly, Stavitsky’s treatment has to be turned on its head, i.e. for very high tau. The flow is from the wave. The water particles in the forward section of a wave move in an up-and-forward direction -i.e. a flow in the up-and-forward direction. In an above reply, I suggest standing in waist deep water and getting hit with a wave. If you shut your eyes you will have a hard telling the difference between the experience (at least initially) and that of being hit with some other flow of water. The up-and-forward flow is what I have referred to as the propulsive flow. With some regret, I have referred to the motion produced from the intereraction between this flow and the bottom of the surfboard as the apparent flow -i.e. what surfers see as flow from their perspective. (Please see Dynamics - Surfing the Force.)

I have not dealt with drag, which is important, nor have I offered a analytical model of the relationship between this flow and the propulsion it produces upon impacting with the bottom of the board (which by the way I believe will require some data collection), nor fins in any real depth.

The above is treated with plenty of illustrations in the ‘Dynamics - Surfing the Force.’ thread.

Thanks,

Kevin

I see very little difference between a snowboard and a surfboard . . . . in both cases there is a force acting on the bottom of the board… . this force is almost entirely due to gravity in both cases. . . . . the mountain pushes against the snowboard, but calling it a ‘propulsive force’ is misleading. . .

.

Quote:

I refer you to the ‘Dynamics - Surfing the force’ thread.

Breifly, Stavitsky’s treatment has to be turned on its head, i.e. for very high tau. The flow is from the wave. The water particles in the forward section of a wave move in an up-and-forward direction -i.e. a flow in the up-and-forward direction. In an above reply, I suggest standing in waist deep water and getting hit with a wave. If you shut your eyes you will have a hard telling the difference between the experience (at least initially) and that of being hit with some other flow of water. The up-and-forward flow is what I have referred to as the propulsive flow.

Kevin

Your example is only true once the lip of the wave has thrown out horizontally. . . which isn’t what we are discussing at all. . . if one stands in the water and lets a wave pass over one , it isn’t at all like being hit by a flow of water. . . the water level rises and drops but doesn’t ‘hit’ horizontally.

Thus your example is completely irrrelevant

.

Space Commander Lightyear,

That reply gave me a certain sense of deja vu somehow.

If you’re talking about the forward (beachward) part of the circular orbit of a water particle in the wave face, that’s

simply the forward (er, beachward) motion of the wave together with the waveform (crest) moving through the water and a bit of (oh yeah) gravity,

not indicative of a net propulsion flow forward (again, beachward) relative to the crest in any useful energetic. Unless you’re trimming upsidedown under the hook.

Much the way the lights in your sneakers describe a forward elliptical orbit when you’re running. Now you wouldn’t be saying that a previously overlooked energy flow quality of the lights in your sneakers make you able to run faster because of the forward component of that cycle, would you?

Or did you just mean that the water that your tail leaves behind makes you go fast like a rocket!!! (?) Cuz that’s awesome.

I’m going to try to take a picture of my “root spray” for you to analyze and see what you think–there’s probably something I’m doing wrong,

Woody

Surfing is a lot like gliding

Now let’s say that we have a glider, gliding along on a fixed glide path . . . . and using the force of gravitational attraction as its source of forwards propulsion.

Next, let’s assume that the air around the glider lifts upwards ( a ‘thermal’. . . analagous to a wave lifting a surfboard). . . now it is clearly the case that the glider will not accelerate forwards and horizontally because the air surrounding it is lifting. . .so it is definitely not being propelled by upwards flow. . . it is however, gaining gravitational potential energy from that upwards flow.

.

Roy

Interesting interpretation, but I believe it to be incorrect. The water particles in a wave are carried forward and up, then back and down. When the wave is shoaling the actual profile does change (its not a circle as in deep water), but until the wave breaks the particles do continue to travel in a loop (however distorted and not necessarily in a closed loop; the circular path in deep water isn’t even closed, but its close enough to be treated as such), the particles in these loops having the characteristics just described - up and forward, then down and back. Water particles traveling up and forward is a flow, as are particles traveling down and back, the two flows forming a ‘loop’ of sorts, if you like.

Thanks,

Kevin

Kevin,

Your example of being ‘hit’ by a water flow when standing in the shorebreak SURELY only applies to being hit by a throwing lip. . . . please don’t try to tell me thatstanding in the water while an unbroken wave moves past is like being hit by a flow of water because it most certainly isn’t. . . the wave just rises and drops without ‘hitting’ in a horizontal direction. . . . surely you have experienced this while swimming???

So what you are doing is taking an example of water being thrown horizontally by a breaking lip and attempting to use that example to show that the miute rotation of water molecules in an unbroken wave exerts a powerful horizontal force, however they are not the same cases . . . . . and your argument is thus fallacious. . . . as you must, hopefully, be able to see for yourself.

Thanks!

Quote:
The water particles in a wave are carried forward and up, then back and down.

Actually the water particles are lifted backward and up and then forward and up as part of the path of the circle. See this animated illustration again and mouse-over the red water molecule to see where the path of a water molecule goes:

http://www.crocodile-clips.com/absorb/AP4/sample/media/DJFPh063waterwave2.swf

Quote:
When the wave is shoaling the actual profile does change (its not a circle as in deep water), but until the wave breaks the particles do continue to travel in a loop (however distorted and not necessarily in a closed loop; the circular path in deep water isn't even closed,

Do you have any reference for these statements, or are you just basing them on your own observations.

Here’s another point:

We all know that that the most powerful lifting force is found in the steepest part of the wave face. . . . however in a vertical wave face the part of the circular molecular water movement which is exposed to the surfboard is downwards NOT upwards. . .

!!!

Quote:

Water particles traveling up and forward is a flow, as are particles traveling down and back, the two flows forming a ‘loop’ of sorts, if you like.

Er, that’s not a “flow” per se if the particle is simply describing that loop from your perspective at profile. If it’s simply a point being that ends up in the same place, just a point passively riding out the passage of a vertical waveform travelling forward under it.

My shoestrings perform a similar pattern when I’m pedalling my bike. Do my shoestrings have a flow you could surf?

I mean, you can call it a flow and you can project whatever dynamic characteristics you like onto it, but the fact is that when I sit on my surfboard and a wave rolls under me, I describe the same loop, with no net propulsion occurring to me or originating from me.

the unbroken wave in a heavy shorebreak will push you back no worries (even lift you up and dump you)

if your standing on the beach

if your actually floating in the water you obviously move with the flow of particles because you are buoyant

but if your fixed on the sand the unbroken wave will seem quite powerful and lift you up

has anyone tried to get out of the water in a heavy shorebreak thats overhead

theres huge forces there but even before the wave has broken theres a lot of push

Upwards but not backwards

.

at kahutara and napier marine parade

when you gettin out and the shore break is heavy

its a nightmare

your just about to get your feet planted when the next wave drags you back out and up

dumps you face first and then while your recovering, the next set does the same thing

i find i let it toss me and try and to land running

it drags you out and up

out and up

in the astute words of the neophyte lyricist.and clinical social anaylist:

bom bom dip da dip da dip

bom bom dip da dip da dip

Lets go surfin now

Everybodys learning how

Come on and safari with me

(come on and safari with…)

Early in the morning well be startin out

Some honeys will be coming along

With our boards inside

And headin out singing our song

Come on (surfin) baby wait and see (surfin safari)

Yes Im gonna (surfin) take you surfin (surfin safari)with me

Come along (surfin) baby wait and see (surfin safari)

Yes Im gonna (surfin) take you surfin (surfin safari)with me

Lets go surfin now

Everybodys learning how

Come on and safari with me

(come on and safari with…)

At huntington and malibu

Theyre shooting the pier

At rincon theyre walking the nose

Were going on safari to the islands this year

So if youre coming get ready to go

Come on (surfin) baby wait and see (surfin safari)

Yes Im gonna (surfin) take you surfin (surfin safari) with me

Come along (surfin) baby wait and see (surfin safari)

Yes Im gonna (surfin) take you surfin (surfin safari) with me

Lets go surfin now

Everybodys learning how

Come on and safari with me

(come on and safari with…)

Theyre anglin in laguna in cerro azul

Theyre kicking out in dohini too

I tell you surfings mighty wild

Its getting bigger every day

From hawaii to the shores of peru

Come on (surfin) baby wait and see (surfin safari)

Yes Im gonna (surfin) take you surfin (surfin safari) with me

Come along (surfin) baby wait and see (surfin safari)

Yes Im gonna (surfin) take you surfin (surfin safari) with me

Lets go surfin now

Everybodys learning how

Come on and safari with me

(come on and safari with…)

With me

Surfin safari

With me

Surfin safari

With me

Surfin safari

With me

Surfin safari

With me

Surfin safari

With me

trite perhaps but a welcome diversion for some

…ambrose…

Now Back to SCIENCE

…who ray?..

when the water clarity is lacking

perhaps we might find solace

and recreation hashing out a few equations?

aw shucks

out of black board space

and chalk.

SKAT…excuse my language

I dont speak french

Propulsion in Surfing In A Nutshell

Figure 1 shows the velocity of a water particle in the face of a wave. The velocity of particle shown has components in both the upward and forward, or toward-the-beach, directions.

Figure 2 shows a flow interacting with a flat stiff surface. Regardless of what paths individual water particles take, the impacting flow will produce a force, P that is perpendicular the plane of the flat stiff surface. The weight, W of the flat stiff surface is included for reference with respect to direction, and in anticipation of Figure 4.

Figure 3 shows how I’ve defined pitch, roll, and yaw for a surfboard. I believe these are more or less consistent with their common usage.

Figure 4 shows both the force P , produced by the flow impacting the bottom surface of some object (say the bottom of a surfboard), and W ,the weight of the object. Both of these vectors are now shown in 3-dimensions. It also shows how pitch, roll and yaw are used. Here, the x direction is the forward or toward-the-beach direction, the y direction is the down-the-line direction, and the z direction is the upward direction.

The final vector equation for this simplified version, is

­R = P+W

Where R is the resultant force.

In the (simplified) trim equation, the vertical component of P is balanced by W .

This resultant force produces the motion of the object, here presumably a surfboard and surfer. I have referred to this motion as ‘apparent’ in my threads Dynamics – Surfing the Force, and this thread, it is the motion the surfer experiences while surfing. It is important to distinguish this ‘apparent’ or generated motion from the flow which produces it.

What’s not included?

1. The exact nature of the relationship between position of water particle on a wave and its velocity, see Figure 1.
2. The exact nature of relationship between the flow and the force produced, see Figure 2.
3. Drag, the effects of fins, etc. have not been included, see Figure 3, and vector equation above.
4. A lot more, like shear effects, etc…

Notes

This treatment was an outcome of my extending Savitsky’s original work on high speed planing (see diagram below.) Basically, in Savitsky’s original treatment a flat surface, call it a plank, is moving across a flat fluid surface, the plank being at a small angle to that fluid surface. This results in a normal force experience by the plank (a force perpendicular to the planks surface.) My extension was to make the angle between the fluid surface and the plank very high, in particular so that the velocity of the water particles would reflect the profile they might have on a wave face.

Regardless of whether or not this treatment was what Savitsky originally had in mind, the significance of his terms or the language he used to describe the phenomena still seemed appropriate, in particular spray root, maximum pressure, etc. , not to mention that his treatment served as an excellent point of departure.

Reference:

“Hydrodynamic Design of Planing Hulls,”

Daniel Savitsky, Marine Technology, October 1964 Issue

Also, my apologies to Savitsky, I seemed to have spelled his name with an additional ‘t’ in prior posts.

Note on Notes on Notes (Added 08/10/06)

More Mea Culpa: “Up-And-Forward” and “Down-And-Back”

Perhaps at some point you will decide to take another look at the motion of water particles in a wave. (From the posts so far, it seems that a few have done as much.) If you do, you will find that there is a lot more to it than my simplistic description of “up-and-forward and down-and-back”. It’s a loop, roughly a circular loop in deep water, and a progressively distorted loop as the wave shoals. Just “up-and-forward and down-and-back” is sort of a straight-line trajectory – please, attribute the use of this phrase to my laziness.

He’s how it evolved; start to explain this treatment (what makes surfboards go) to someone. The first time you do you might decide to be far more detailed in your description of the motion of water particles in a wave. At some point, particularly if you’re at the beach, as the person that you describing the motion to, eye’s begin to glaze over, you might choose to short-circuit your description and simply point to the motion that some duck, sitting just outside the line-up, is experiencing as a swell passes underneath it, and say, “See! Sort of up-and-forward and down-and-back.” After a while, the phrase just sticks.

Regrettably, I suspect there is more of this kind of laziness to be found in what I have written so far, though hopefully, not much more. Luckily however, that the motion of water particles in a wave is more complex than up-and-forward and down-and-back doesn’t change anything.

I suspect just about any introductory physical oceanography text has a pretty good description of what is going on in detail. (I actually don’t know that for sure, it just seems reasonable that they would.) Though likely somewhat out of date, my introduction to the topic was “Wind Waves” by Blair Kinsman, circa 1960s (?), which I picked up at a local used bookstore and have since lost. Don’t hold me to it, but I think at some point Blair even discusses breaking waves.

Kevin