As a aprt of the educational side of the ROV project, I've been thinking on making a few writtings about flow mechanics in general, and hydrodynamics in particular.

I think that a low level explanation, addapted for non especialists or under graduates, could be interesting.

My idea is centering on the physical model more than in the math, allowing for any reader with any level to undertand the principles.

Anyway, before seriously thinking on starting, I'd like to know if there would be any interest from you.



Hi Ion

I would be interested in learning more. I don't have any background in this area but a curiosity to learn more .I had other ideas about propulsion away from motors and thrusters but they are the only game in town right now using rigid materials.If one were to streamline the ROV to mimic a glider or fish then perhaps flexible components could be used to achieve this aim.



I would love to see that! -- Particularly, I think it would be really great to see some demonstration of how drag effects from turbulent flow around a blunt trailing edge are much more significant than the effects of a blunt leading edge. There really doesn't seem to be any clear and not-intimidating-to-beginners illustration of this sort of thing on the web. I'd love to see, for instance a comparison in overall drag between geometries that look like this:


Hi Erik:

My intention is starting from the beggining, anyway ......

You are right, most explanations are always very mathematical. As you surely know, those mathematical models have, in fact, a little physical meaning, but allow for tools for making very accurate predictions.
Around your question, you've surely found calls to Kutta-Joukowski, and/or Prandtl models. Both are accurate, but supposing that there is an orbital motion of fluid around a moving body, or that lots of mini-eddies are rotating all around its surface, look to be too abstract.
More "physical" explanations can be given, but do not allow, by now, for the development of accurate, validated and solvable mathematical models.

FEA procedures are mostly based on partial solutions for the Navier Stokes equations, and lately on the Lattice Boltzmann models, but as above, are hard to be understood.

Let me try a simple explanation from a more "mind friendly" point of view.

From now on, speeds are relative to the body.
We dont mind who moves, but how the fluid moves with respect to the body.

We'll see the whole thing in 2D. The explanation is equally valid, but a lot easier to be written and understood (My apologizes for my English).
From now on, the word "particle" will be related to anykind of fluid element, sample or unit, and must not be taken in the literal sense.

Let's remember the very old concept of Displacement. It was stated by Archimedes long ago, and almost everybody knows it.
But the Archimedian concept is only related to statics.
What happens to that displaced fluid when the body(or the fluid) moves ?

Nothing in nature happens instantaneously, a time is required for any motion.

When a body moves through a fluid, as Archimedes said, a quantity of fluid equal to the body submerged volume is displaced, but .... where and how does it go ?

Fluid is pushed ahead of the body, and moved appart, around the body, the fluid is holded apart until the body passes by, and the hollow is closed behind it.
Hence, a hollow is created, kept during a time and closed behind the body.

Lets have a look to that part of the flow that is flowing in contact with the body surface between the leading and the trailing edge.

The fluid "particles" just in contact with the "skin" due to the rub on the surface are almost, or completly stopped (In the mathematical world they are considered stopped), but if we go further from the skin, we'd soon arrive to an area where the flow speed is that of the non disturbed stream(Free Flow).

Another interesting thing is that the change is not abrupt but gradual. It looks like if there was anykind of force that holds all parts of the fluid joined, avoiding their free relative motion.
Think that if there was no force of this kind, the particles just over those in touch with the body, and not affected by it, would move with the free flow speed.
Hence, there is a kind of "coalescence" force between the fluid elements. A kind of drag or attraction between the parts.

We conclude that the fluid that has been pushed apart, around the body, moves with different speeds depending on how far, from the body surface, they are.

In the ideal wold, this displacement Hollow, would be instantly created ahead and destroyed astern, but in the real world, everything is delayed.

It can be observed, that the hollow is not instantly closed behind the body, but that, in fact, follows the body, closer or further, depending on a number of things.
Hence, once the body has passed by, the hollow is still there.
Why ? Becouse a time is required for the fluid particles to refill the hollow.

The shape and extension of the hollow following the body, will depend on fluid properties, enviromental conditions and body shape and texture.
The motion of the flow refilling the hollow gives place to what is known as the wake or trail.

Lets now have a look to the figure posted by Erik:

The only difference between bodies BD and AE is the lenght. In another explanation we could see how this affects the flow conditions. Body C is an anti-flow body.

FIGURE E Blunt trailing edge]
Flow collides with the flat leading edge.
At the same time it is taken apart, some areas bounce back against the main stream, leading to eddies formation, but very shortly fall into a tidy free flow area that sweeps them downstream again around the body.
It can be said the the life period of those eddies is very short, due to the vicinity of the tidy area and the high speed zones around the body where they are swept.
At the trailing edge, the sharpened shape allows for a gradual closing of the hollow. Very close after the body, the hollow shape is almost only a line.
The fluid around the body (Upper and lower streams from a 2D point of view), take a "Normal to the flow" slow speed. It moves slowly for refilling a little hollow, and hence, into ideal conditions, when both streams meet, relative collision speed is very slow or null. Little, eddies are induced.

FIGURE A, Blunt trailing edge]
Now, incoming flow is smoothly taken apart, and then, little speed is lost and little eddy formation is induced. Hence, flow arrives at "full speed" to the blunt leading edge.
A very big trailing hollow will then be following the body, with a very abrupt pressure drop.
The flow collapses behind the body, leading to a very big mixture between the upper and the lower streams. Some parts of the flow will eventually start moving against the general stream.
As there is a big "empty" volume behind the body, no flow is present for dragging and inducing a tidy state again, as it was in the former case trailing edge, and hence, eddies life period is very long.

The wake is a lot longer and stronger than in case E.

Drag is nothing else than an expresion of the energy stolen by the fluid from the body. The more energy is stolen, the more drag is measured.
And ... How is that energy stolen ? In the form of motion and heat.
The more the fluid motion is changed, the more fluid volume is affected, the more energy has been transfered from the body to the fluid.
In the case A, eddies are stronger, and their life is longer, hence more drag is induced.

Hope this explanation can be useful.



CFD Flow around figs A and E.

For other flow conditions results may change.

Colors are related to local Re


Hi James.

Tanks for your interest.

Sharing knowledge is always good.

If there is no more interest in the Forum around this topic, I'll not make the writtings (dont want thewhole forum getting bored). Anyway, here or by private messages, I'd be glad helping you as far as my knowledge could reach.



Hi Erik:

I've been busy last month. Now, I hope I'll have a little bit more free time.

As nobody commented my last post on this thread, I did not take the trouble to write or explain anymore about the subject.

Anyway, now that I have some spare time, let me tray a lot simpler explanation, that may be more useful.

Let's neglect viscosity, and let's restrain the whole question to uncompressible fluids.

This way, there is no need for any CFD use.

Now, under those conditions, flow speed has no remarkable relevance, and the question can be observed from the "shape only" point of view.

Case A seems to be the most general. So, let's have a look at it.

Flow arrives to the leading edge with a speed vector, Vinf (Free flow velocity).

While the fluid travels around the shape, the local speed vector (Va), has to rotate in order to addapt it's direction to the surface.

As energy MUST be conserved, that rotation involves a loss, that decreases the modulus value of Va.

If Va decreases, the local pressure value increases.

Around shape A, speed gradient is negative, and hence pressure gradient is possitive. Consequently, pressure gradient works against flow.

Around shape E:

Upper and lower flows join at the trailing edge and velocity "recovers" its initial speed and direcion.

Minimum speed and hence maximum pressure is located at the leading edge.

Hence, velocity gradient is positive and pressure gradient is negative.

Pressure distribution favors the flow.

Normal component of local velocity, takes it's role when surface drag is taken into account.

For all cases, the smoother the pressure-velocity gradient the better. This is one of the factors in the relevance of the lenght to beam ratio.

If viscosity, boundary layer effects, turbulence, surface properties........ etc are included, each shape may be better or worse depending on the enviromental conditions.




This is great- and my apologies for not answering back... your explanation (and simulation) were very helpful for understanding what's going on and I'm not sure how I missed getting back to you after the first post. For me, the thing you said that really sums up what's going on is "The more the fluid motion is changed, the more fluid volume is affected, the more energy has been transfered from the body to the fluid.".

I like thinking of it that way: the more a fluid has to move out of the way or change pressure, the more drag there will be.

I've been continuing to work on ideas for how to efficiently move through water without sacrificing a forward surface that is easy to mount cameras, lights, etc too. It seems to me that as long as a vehicle has a well-tapered trailing edge, the difference between an elliptical nose, a flat nose with rounded corners, or a flat nose without rounded corners is small by comparison.

Is the ratio of leading edge drag to trailing edge drag of an arbitrary geometry greatly different at different reynolds numbers?

It's always great hear your thoughts on this stuff!

Thank you,



Hello Erik:

No worries ...... :-)

The key is a lot more in the Lenght to thickness ratio than in the shape itself.

For the conceptual stage of a new design, both kinds of drag must be mentally separated.

The explanation below is related to a body with an arbitrary shape.

Skin drag is due to the shear stress between fluid layers moving around the body.

If fluid velocity is measured from the body's surface. along a normal to that surface, to a given distance, the speed distribution will result to be parabolic. Being zero at the surface, and "equal" to the free stream velocity at a given distance. This is what is named as "boundary layer"

Surface drag and shear between fluid layers, due to viscosity lead to this distribution of velocities.

Hence, and once again, if fluid motion is changed, energy has been stolen from the system. This energy is being used to overcome the shear stress that viscosity develops between layers.

Notice that in all the explanation above, its supposed that the fluid moves around the body in a streamlined way, without anykind of separation. It means.

This flow condition, only happens at low Reynolds numbers.

How to minimize skin friction ? Minimizing surface or reducing flow speed.

Let's increase Re a little bit.

Now, some eddies start to develop around the trailing edge. Flow separation is starting.

At some places on the body skin, the fluid is no more following the shape. It's speed does not allow the fluid for changing its direction on time, and dynamic effects (Inertia), prevail over viscosity effects.

Please note that the relation between Inertil and viscous forces is the definition of REYNOLDS NUMBER.

Now, a pressure gradient is developing around the body, and leading to a new kind of drag, the pressure or shape drag. From the energy point of view, those new eddies are stealing energy .....

What part of drag belongs to skin and what to shape ? It must be calculated for each particular shape.

The faster the body moves, the sooner the flow will get separated from the body skin.

The first effect is that the trailing edge "wake" starts to enlongate, behaving as if it was "elastic".

Moving faster, the trailing edge eddies become unstable, leading to a turbulent configuration. (More energy is wasted). The body wake extends a lot behind it, meaning a lot of fluid is being "disturbed".

Moving faster ...... fluid behind the body, moves backwards, trying to fill the "hollow" left by the body. The interaction between that returning stream and the free stream around it, lead to the formation of one or more "eddies chains". Many eddies joints, distributed along lines, following the body.

The more eddies, the more wasted energy ......

Lets increase speed even more ...... at Re=2 10^5

The boundary layer itself (That zone in contact with the body skin where flow speed distribution was supposed to be parabolic) becomes turbulent. Instead of that "tidy" area, we now have a turbulent thin layer sorrounding the whole surface.

Skin drag almost falls to zero, and flow around the body improves. Think on those micro-eddies, as a joint of wheels set on the surface. The flow, now, does not have to overcome layers friction, but only slide on those "wheels".

This new boundary layer allows the flow for smoothly sorround the shape again. The wake field becomes narrower and pressure drag decreases.

Moving even faster will brake that turbulent boundary layer, a shock wave would develop ahead of the body, and turbulence would lead to unstable conditions and really high drags.

As boundary layer separation, happens due to pressure gradients, the way to avoid that is designing smooth shapes, where speed and pressure gradients are always below certain limits, that can be deduced from the Re.


A pressure distribution which avoids the boundary layer separation is the way to go.

That leading to trailing edge drags relations you asked for, will depend on Re, shape and dimensions proportions.

In the attached pic, there is a tipical example. The comparison is between a cylinder, and the same body with a shaped "tail", made in the turbulent boundary layer separation range, where almost all drag comes from the pressure field. The shorter the tail, the higher the pressure drag. For slower motions, where skin drag becomes significative, skin surface has to be reduced, or some kind of "turbulator" fitted on the body, for helping on the early development of the turbulent boundary layer.



Some quick ideas for improving underwater efficiency:

Grant the propellers for being fed by clean tidy flow (Will improve props and batteries performance)

Avoid, where possible, glass-like surfaces finish. I would try some level of bumpy texture that would help for a thin turbulent boundary layer development at low speeds.

Avoid hard chined angles. Allow the fluid to follow the surface shape.

Avoid dynamic pitch, roll and yaw --> Try a shape as symmetric as possible. Pressure distribution changes with speed, and hence, balance possition of the ROV changes as well.




First thank you so much for you information that you have posted regarding hydrodynamics. I would be interested in learning more.
Work has been very busy the last few months it is now lighter so I have some time to respond and design time.
My ROV is has incorporated many of the points you have listed in your postings EPPLER 863, center of buoyancy and center of gravity, thruster shroud profile, and motor placement just to name a few.

Most of the ROV is 3D printed PLA plastic the size of profile is 11.2 Inch (maxinum of X axis of printer) X 7 length of E tube.


558-ROVFISHIIver1.jpg (188 KB)


WOW ¡¡¡

What a great, smart and nice design ¡¡

May I know which profile did you choose ?

As Erik guessed above, the performance difference between the elliptical and the circular leading edge section, will not afford the building complexity in the ROV operating speeds.

I mean, you could simplify your design(if you want), by removing the transparent elliptical cup at the bow of your ROV.

By the way, I think it would mean an optical improvement as well.



Main body is using EPPLER 863 STRUT AIRFOIL-80-scaled to 11.2 inch in length.
Rudder is also using a stretched EPPLER 863 STRUT AIRFOIL-80.
Thruster housings are using the duct profile TPN7516 at 75mm as specified your PDF document.
Thruster Supports (4) are at 45 degree angle with edges radius I am open to suggestions on optimization this and other aspects of entire design. Not breaking when dropped is an important factor.
Thruster cone is at 63 degree angle with radius.
The electronics tube has outside tube diameter of 3.75 inch this will allow using Silicone Canning Jar Gaskets to seal not subject to fluctuation of tube manufacturing tolerance.
In the space between electronics tube and front foil is for the horizontal thruster for crabbing motion not shown on print. Side panels are not shown.
So far so good at half way point as the design is symmetrical printed one side.
I am also adding a golf ball dimple pattern to profile shape.
Thanks again for the wealth of information contained your postings.


Hi all:

Dear Mark. I feel proud of your use of my comments. Thanks a lot.

A comment on your ducts arrangement.

I told you I was going to check what flow pre-rotation angle would be nice for lowering the required propeller torque without a remarkable drag increase.

The way is designing the duct supports in such a way that water starts rotating before arriving to the propeller disc.

This arrangement will decrease the required motor thrust, and hence will make batteries life longer. But at the same time, drag will be slightly increased. The relation between both effects is the key. If drag increases too much, the advantage of pre-whirl, will be lost due to drag.

The way is:

Minimizing surface drag: Minimize number and surface area of the supports.

Minimizing supports pressure-shape drag: Fair both, trailing and leading edges.

Pre-rotating flow:

The pre-rotation angle is a tricky thing. Water flow that arrives to the blades has a velocity that results from the combination of Advance velocity, propeller RPM and radius.

The resultant vector makes an angle with the blade, that combined with the pitch angle at the given blade section, will give the section Angle of Attack.

Each section, yes, even in those very little model propellers, is designed for giving the best performance (Best lift, lower drag) under given conditions of fluid speed and angle of attack, while avoiding cavitation and allowing for best mechanical strenght.

When Advance velocity and/or RPM are changed, fluid conditions at the blades change as well, and hence the whole propeller behaviour.

Thats why a propeller must be tested in the "Service Conditions". Results coming from other conditions testings, with no other technical information, will say nothing about how the prop will work when conditions are changed.

The lower advance velocity, the faster the prop turns, the bigger the angle of attack.

If the angle of attack is too big, the "Boudary layer" (See former post), will be swept, and separated, the blades will start to stall.

If the angle of attack is too little, the lift component, the one that produces Thrust, could change it sign, and become negative.

As the whole comments above are related to a given section of one propeller blade, the NET thrust can be possitive, albeit it could be negative at some sections.

The result is a drastical reduction of the blade performance.

Flow pre-rotation allows for optimizing the conditions at each section of the blade for the service conditions by adjusting velocities and angles of attack.

The problem is that there are so many variables involved in the arrangement, that making mathematical predictions is more a matter of fortune-telling than of sciences.

Dear Mark, Im trying to build that Mathematical model (Hahahaha, yes may be Im a little crazy, I love maths). As soon as I have something reasonable about pre-rotating supports, I'll let you know.

Yes there are comertial ones, but for very big ducts, and .... when speaking about fluid dynamics, scale matters a lot.



For anybody interested ...........

Check this ..... "Marine Propellers and Propulsion" (John Carlton), PAG-15




Cleaned up a nozzle supports and for this go around using same prop as stock ROV when testing will pereform verification in situ (open water with scale attached to rov).
Thanks, Mark



Your descriptions are always awesome to read. I actually feel like you've done a better job describing what's happening at a conceptual level then the profs during my undergrad did. Everyone always wants to move straight to the math without first making sure students understand the concept. For me, understanding the concept first is essential.

Thank you for the continued education. I'm sure a lot of people are benefiting from it.



Thanks a lot Erik.

I agree with you, and that's the way I think technical education would have to follow.

Concepts before maths.

Maths are nothing else than a fast and efficient way for concepts expression. How can an unknown concept be expressed ?

But .... Its like magics. When the idea is clear, maths become an easy stuff.

Regards and thanks for your appreciation



As I said at the beggining of this thread, my intention was, and is, giving all interested members of this comunity a brief view around general hydrodynamics. A brief, but hope, useful view, able to be understood by everybody.

Many Open Rovers may have a deep knowledge about the subject, my intention is making the explanation for those having a little or no previous knowledge. Of course, and has far as my knlowledge could reach, im for entering any deeper question that could be of the interest of any of you.

NOTE: Many conceptual simplifications will be done and rough examples used. Dont hersitate asking for clarification or more accurate explanations.

OK. Lets go for the basics.


Whats a fluid ? Best way for starting a mental model is the Newton's concept. Yes, the same Sir Isaac Newton we all know.

Lets imagine matter builded from tiny "bricks" that are linked together. Yes, molecules or atoms. Their relative positions and distances are fixed. No "brick" is able to move with respect to the sorrounding ones. That's why its a SOLID. All constructions elements are fixed at their positions, a solid can only be moved as a whole.

What happens if that solid is broken in, lets say, two pieces ? We've got two solids, having each one the same properties than the original one.

From a mechanical point of view, that force, that holds all bricks together, may be said to have two main properties; strenght and range.

Suppose the case of glass, and suppose a glass bar subjected to a traction force. It will not elongate even a bit, but once a given force is achieved, it suddenly brakes with no prior elongation or distortion.

Lets now think on an steel bar. Once the stress starts to work, the bar starts to elongate. Elasticity comes into play. Steel will not get suddenly broken as glass did, but will get more and more distorted, until achieving the stress limit.

In the case of glass, the "bricks" linking force is very strong, but its range is very short. Just by taking the bricks a minimum distance appart, the force is exceeded.

In the case of steel, the required force may be lower, but .... the bar can be a lot elongated before braking. Its elasticity can be interpreted as if the "bricks" where linked by forces that have a very long range, which are able to keep "things" joined even through certain distances.

What about liquids ? The same bricks, joined by the same forces ...... but. Now, those building bricks mentioned at the begining, are linked in such a way, that are allowed to freely move, but always keeping their relative distances.

If all components can freely move, a liquid does not have to keep a given shape. In fact a liquid has no shape. It's shape will adapt to that of the container where it is kept.

But, as the distance between "bricks" must be always the same, the volume of the liquid will also be constant.

Think on real bricks. 50 bricks, put togheder in an orderly way, will have the same volume, no mind the resulting shape of the joint.

What if neither the "bricks" distances nor the location are holded ? Then, the resulting matter will be free to addopt any shape, like liquids, but also to addopt any volume. That's a gass.

Solid, liquid or gass, are nothing more than an expression of the degree of freedom of the matter components.

When the mechanical behaviour of a solid is studied from the engineer point of view, it is seen as a whole. Most calculations made around solids do not mind on the shape, but in general concepts like Center of Mass, material properties that are supposed to be the same through the whole body, moments and forces, punctual vectors ...... and all related most times to a given material quantity.

Solids most times, can be studied as units, as bodies that have a given mass, volume and shape. For example, only four numbers can define a solid motion, XYZ velocity vector and time stamp.

In the case of fluids, things become a lot more abstract, and hence, related maths a lot more complex. But ..... lets go slowly, math makes no sence if there is no concept to explain.

For an enclosed fluid, obliged to addapt to a container shape, things are easier, but ... what about open free fluids ?

When studying a fluid behaviour, no borders can be used most times. A moving fluid, the wind, the ocean, has no shape, no starting or ending point. Where are the borders of the water that sorrounds a sailing ship ? There is no defined mass, and hence, none of the properties that classic mechanics apply to solids.

Then, how to approach the fluids study ? It must be assumed that a fluid is a continuum, meaning that there are no defined limits, and hence, no defined dimensions, no begining and no ends.

The way to approach a fluid is the counter than approaching a solid.

While the solid is studied as whole, and how it is composed is a secondary question that can be deduced from the whole, fluids are studied from the components (the bricks) and the whole is deduced from the parts.

Studying how each "brick" behaves, and how each one, is influenced by all the others, allows for knowing how the whole fluid will behave.

NEXT: Free flow, internal forces.


Hi Mark:

Im at my holidays place (Europe West Coast). I have no means for making any serious study here.

I've required some technical information to Graupner and PropShop about the propellers, but the technical Dpt at both places is on holidays as well.

As soon as I get that information I'll try to optimize the thrusters internal supports design.

Depending on that technical information, the pre-rotation of fluid would have to be different.

Has anybody here, ever checked what is the average blade section profile of the Graupner propellers ?

Depending on that profile, a slight pre-rotation of the inflow, could improve, or not the propeller performance a lot.