Scaling power to weight ratios from human power to models

[Skip Johnson]

I'm getting ready to build a couple of models to compare a couple of drive technologies.

I have two matching 6-volt gearmotors left over from building a working Fallout door for my youngest granddaughter, Motors draw about 0.2 amps under load. The problem is how much should the model(s) weigh to semi accurately represent a solo pedal powered boat.

Say the boat weighed 260# and the powerplant can sustain 100 watts. that gives a ratio of 2.6#/watt.

If it's a linear ratio, then the model should weigh (1.2*2.6) ~ 3.12#

Seems reasonable, is it?

 

[philSweet]

No, it's not linear at all. You have to decide what exactly you want to model. What are the two drive ideas? Sometimes, you can make a reasonable assumption that the relative performance of two systems will behave better than the absolute performance of either.

I'd also point out that hundreds of really solidly engineered pedal boats have been made over the past century, and there is a lot of info available. These range from world record sprint speed boats to solo, pedal-across-the-Pacific. It's a biggish design space, but it has been thoroughly investigated.

 

[Skip Johnson]

What I want to do is compare a contemporary pedal/paddle drive commonly used in the MR.340 race with a pedal driven horizontal oscillating fin located under the GC of the craft.

The issue is to match the power to weight ratio of the models to a solo marathon racer. Too light or heavy a model tells me nothing.

 

[fallguy]

Hey Skip

~ I don’t profess expertise, but enough curiosity to stir experts; perhaps.

Lots of ratios come to mind, but to effectively compare the two propulsion systems; I’d say you need more than weight. Perhaps this is a no brainer for you; if so I apologize if at all patronizing.

Other ratios to consider…

Displacement
Waterplane
Obviously hull shape.

Froude number which is speed and waterline length driven should be the same or very close.

You are driving the weight based on the power to weight, but the Froude number is waterline length and Velocity.

So, I think you need to focus on more than the weight to start.

But I’d start with estimating the velocity.

A man of your wisdom can probably guess closer than me. From there you establish the vessel length. Then you can establish a similar l/b ratio and ultimately see if you can build the model. If the 260 number includes a pedaler; perhaps you can use the mass of the pedaler as a variable for data collection?

These are my fairly crude thoughts.

Dan

 

[Skip Johnson]

My wisdom is suspect, I once fervently believed that a catamaran would never be the best solution since such a craft automatically starts out with a ~41% penalty in wetted surface verses an equivalent shaped mono hull.

Since the model boats will be identical (shape, displacement, wetted surface.....etc. including the motors the only variable is the drive mechanism; either paddles or an underwater horizontal fin.

IF the power/weight ratio is scaled correctly it should be fairly easy to decide which approach to spend the time developing full scale.

 

[Ad Hoc]

My wisdom is suspect, I once fervently believed that a catamaran would never be the best solution since such a craft automatically starts out with a ~41% penalty in wetted surface verses an equivalent shaped mono hull.

This is where "scaling" breaks down.
A catamaran, has significantly less residuary resistance than a mono, as such, in Fn from 0.5+ a catamaran has much less resistance, by up to 50% than an equivalent mono.

Thus your model scaling...you need to understand are you scaling "just" the drive train...or the whole model + drive train.
There is a multitude of laws/ratio mixed into this "simple" scaling.

Thus what is the objective.

 

[Skip Johnson]

My previous opinion re mono or catamaran hulls was based on both being long slender things with semicircular cross sections. I've run Michlet/Godzilla optimizations to find the sweet spot where the sum of wave and viscous resistance is at a minimum for a particular displacement and speed profile for a very long time now for a multitude of human powered craft.

My objective now is to compare two different mechanisms; paddle driven or horizontal oscillating fin, in order to decide which path to take in a quest to set a new distance in 24 hours record.

Trying to scale up data from such models is a fool's errand, I just want to trial the drive systems in a rational manner to help make that one decision. If power to weight ratio scales one to one the 3.12#+/- model boats should be "impedance matched" to the full-size thing close enough to help make the decision.

 

[portacruise]

Maybe this guy can be of some help on scaling, he's always comparing efficiencies some with different scale models,

 

[fallguy]

IF the power/weight ratio is scaled correctly it should be fairly easy to decide which approach to spend the time developing full scale.

You’ve got Ad Hoc participating so I’ll only offer my dime for fun.

I’d be more interested in making sure the Froude number and l/b ratios were the same. The weight to me for the model is fairly unimportant (within reason), ceteris parabis. But to scale the model, I’d want to estimate the velocity and calculate the length/beam and build to that. And I’d be more concerned about whether the velocity is linear. I expect a riderless model to do a bit better, but in my brain the power to weight of the original to the models is not vital to compare the two drives. But the Froude number and the l/b ratios need to be close. Consider, once the shape is established; you can add a mass to the model for testing…but the model shape is much harder to change.

And, if you cannot scale the mass; you are still comparing the two drive systems with a similar vessel. (I doubt you cannot scale the mass, which would mean you cannot build the ship light enough). In fact, I’d say there is a good likelihood you have to add weight and you can design the ship for it.

All the best; I’ll return to my corner.

It was a pleasure meeting you. Next time you are here, we will take out the Redfin.

 

[gonzo]

The problem is that when the ratio of the scale is large, there are some things that don't change and affect the results significantly. For example, viscosity of water, gravity, and start of turbulent flow (Neusel or Bernoulli).

 

[Skip Johnson]

The problem is that when the ratio of the scale is large, there are some things that don't change and affect the results significantly. For example, viscosity of water, gravity, and start of turbulent flow (Neusel or Bernoulli).

Thanks, that helps me keep things in perspective. If this thing goes forward, it will be interesting to see which branch we take. On the one hand there's the paddle drive system that's well developed and proven. In the other corner is a theoretically promising approach that would require a great deal of time and effort to optimize.

The function of the models is to help make a rational decision as to which path to take.

 

[tropostudio]

What I want to do is compare a contemporary pedal/paddle drive commonly used in the MR.340 race with a pedal driven horizontal oscillating fin located under the GC of the craft.

The issue is to match the power to weight ratio of the models to a solo marathon racer. Too light or heavy a model tells me nothing.

The MR340 looks like a crazy race! What amazes me is how relatively close the record times are amongst solo vs teams, and by paddle vs pedal.

340 miles covered in under a 40 hours by a solo paddler or pedaler is 8.6 miles/hour. I assume your baseline of 100w and 260# figures means you are looking at a solo vessel. What are the nominal continous boat speeds discounting rest breaks and current? FWIW, the crew that just broke the Missouri River Speed Record averaged 3.94 mph. I think their speed picked up by 1-2 mph after they got past all the dams in South Dakota.

The formula for a 'Froude scaled' power conversion uses the formula P model = P full x (1/scale factor)^3.5. The thread Scaling power?(with replies by @Ad Hoc) goes there. Becasue it discounts viscous drag, the results are exceedingly low. One would imagine boats in the MR340 are at SL of ~0.8 - 1.2, with skin friction making up over 50% of total drag. Does that sound correct?

Do a search on model boat building, and you come across rules of thumb of 1.5-3w/lb to push a displacement model at hull speed. Nothing specific about the model scale, but applied to your scenario, that might be applicable.

How long is your boat gonna be? How about 20' LWL? A 1/5 scale model will have 4' LWL. Model displacement will be 6.4#. 1.5w/lb x 6.4# = 9.6w. Halve that or double it. Quarter that or quadruple it. Model up both a 'proven' paddle drive and your horizontal fin drive. Put in a PWM controller and measure power consumption at a range of SL's for both drives in the same hull model. If there is going to be signifigant improvement in going to a different drive, I'd think it would show up. If your hull shape and the model for the existing paddle drive is scaled to an existing boat with known performance, you could draw better conclusions. Seems like a fun project!

Also, the video @portacruise links to is worth a look. The model may be 'clunky', but the efficiency of air props over putting the drive in water is marked - see screen snip below. There is mention of MIT's Decavitator as well.

 

[Skip Johnson]

Many thanks, if you look closely virtually all the records occurred one year when the water was high. Paddle vs pedal continues.

You are correct viscous (skin) friction makes up a significant portion of the drag. I use a little shareware program Michlet/Godzilla by Leo Lazauskas (who coincidently reappeared on this forum after an extended absence) to find a shape that has the minimum drag for a specific displacement and speed profile.

Your rule of thumb is exactly what I was looking for, and I really appreciate the info. I dropped out of model building years ago but one of the lost references from a tornado a few years ago was a well-worn booklet by Vic Smeed. I'm looking at less than 1.5-3w/lb, more like .4w/lb but it is a low powered human craft we are scaling to.

The solo boat will be closer to 30' lots of details yet to be determined. But the model issue is now pretty straight forward. If I can develop the model horizontal fin drive to the point that it seems practical, I'll build an identical model with the identical motor with a paddle drive and compare the two.

 

[tropostudio]

Optimizing the hull is one challenge, and optimizing the drive is another! And doing it all with very low power input makes it even more difficult. You know how it goes- improvements are incremenatl and hard won. You've built a lot of boats, so must know building a big model isn't necessarily more expensive or time consuming than fretting over a small one. Good luck, and show it it off when it doesn't have to remain top secret!

 

[HelmutSheina]

Some thoughts on the paddle one, maybe consider SUP style paddles with wide short blades, and put cupping in the blades, which might also help with a cleaner exit at the end of the stroke. Also streamline the paddle shaft.

Have you seen this one?

Presenting the Amazing Pedyuloh

Facing Forward, Pedaling an Efficient Yuloh (!)

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