Scale model power calcs -

Discussion in 'Boat Design' started by rwatson, Apr 16, 2009.

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rwatsonSenior Member

I am building a 1/10 scale model of a 28ft power boat, that should do 20 mph with a 75 hp motor. For testing, I want to have a comparable power source for the model.

I came across some formulae (attached) which claims to do this.

It would be good to get some feedback on
a) the validity of the assumptions
b) the accuracy of my results

In "spreadsheet talk", I figure it should work like this.

If the full scale boat will needs a 75 Hp engine, according to the formulae, the scaled down power (in watts) required for the model would be :-

= (1000 x 75) / ((sqrt(75) * 7)

or 1237 watts (Given there are 745 watts per hp, nearly two horsepower)

The scale speed for the model works out to about 6.5 mph .

The formulae sort of makes sense to my mathematically challenged brain, but the power formulae doesnt seem to take into account the scale (1/10th) of the model.

Should I adjust the power calculation by the model scale? Can anyone make any sense of the calculations?

All thoughts welcomed.

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2. Joined: Oct 2008
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rwatson

when you say should do 20mph with a 75hp motor, is this just a "guess" or a known fact?

What is the displacement of the 28ft'r?

You have to be very careful when scaling, especially at high froude numbers, since the frictional resistance can vary a lot with minor changes.

You can pro-rata powering based upon displacements easily enough, but when scaling it is totally different, unless as you appear to be, using an empirical based formula that attempts to cover all bases. As such is subject to many caveats...

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rwatsonSenior Member

Yes, that is a known fact - the speed and the power for the full size boat. The displacemnt is around 1400 kg

I understand that the gap between model and full size is fraught with "gotchas", so I am happy with the "approximation" in any system.

If there are any other means of calculating the values, I would be keen to hear about them.

Last edited: Apr 16, 2009
4. Guest625101138Previous Member

The estimated model power looks to by out by a factor of 50.

Both hulls will operate in planing regime. You would expect comparable lift to drag ratio although the lower Re# of the model will cause it to be less efficient in this regard.

If the lift to drag ratio was constant the 1/10th scale model would have 1/1000th the drag of the full scale version.

The nominated speed ratio is 6.5/20 = .325.

Combining the drag reduction and speed reduction a first approximation for the power on the model is:
Model Power = 75HP * 746 * .001 * .325
= 18W.

You could expect a little more than this as the prop will have a lower Re# so less efficient as well.

To put your numbers into better perspective the 1237W at 6.5mph will produce a thrust of 20kgf at 50% efficiency. The model will weigh 1.4kg. So it has enough thrust to pull 14g - better than any rocket that has ever been built I suspect.

A point on practicality. If you have a lightweight full scale boat then building a 1/10th scale model with its own power will be extremely challenging. It could easily be too fragile to handle. You need to go up to about 1/7th scale to get something that does not need ever dob of glue weighed. 1/5th scale will be robust and easy to build.

Also you can get a light weight 1.3kW motor but very hard to get the motor and a battery or fuel source combined with a weight less than 1.4kg - means the hull has to be weightless. But then I am very skeptical about the scaling formulas that suggest 1.3kW for a 1.4kg boat to do 6.5mph. I can push a 100kg boat to 6.5mph with 120W.

Rick W

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rwatsonSenior Member

Thanks Rick - that is a great explanation, because I can follow it . The logic is obvious once its is explained. 1200 watts seemed way off the mark to me.

My best information is that the scale weight is calculated by the cube of the scale, from Sam Devlins book on boat design. (He has used that method to build many full size boats from scale models, and is in line with your figures)

ie. 1/10 scale, (10 x 10 x 10 ) x weight.
This puts the half finished hull (currently .5 kilo without most gear) at about 500 kilo, which is right on the mark. That was building with 1/8 WRC, and 6oz fg/ and epoxy on both sides (and lots of filler). Its a very sturdy hull and can support say 3 telephone books

If the model weight tops out about 1.2- 4 kilo, that will be perfect, as the full sized boat should come in at that about 1200 - 1400 kg.

I would be interested to get any other insights that may come to mind.

Many thanks for the time to explain.

for my reference, the formulae are found at the link
http://www.kakaliproductions.com/eBoat/information.htm

Last edited: Apr 17, 2009
6. Guest625101138Previous Member

Your calculations on the scale weight are correct. It should end up at 1.4kg.

I have found such a low weight challenging for a self powered boat. You need motor, battery, prop and shaft, receiver, rudder, rudder controller, GPS for speed recording, a meter for voltage reading and a meter for current reading. All this in something that keeps the electrics dry and can take a little punishing.

You can reduce some of the metering by timing over a set distance and assuming constant battery voltage but this brings in errors.

You can tow the model but it is not easy to eliminate other factors. Also one of the learnings from the model is how it behaves in waves.

I have had good success with model parts from this place:
http://www.hobbycity.com/hobbycity/...ucts.asp?idCategory=82&curPage=2&v=&sortlist=
The little 3-phase motors are brilliant and the radio stuff good value although I like to buy when the exchange rate is more favourable.

Rick W.

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JoakimSenior Member

For a planning boat the simplest way to estimate is by using a "power coefficient"

V = C * SQRT(P/m).

If you use "marine units" V (kn), P(HP) and m(tn), C is typically between 3-4 (for "normal" boats). C contains all efficiencies, thus P is the engine power. Deriving from that:

P = V^2 * m / C^2

Using m=1.4 tn, V=17.4 kn you should only need ~50 HP engine for that speed.

Using the same formula for the 1:10 scale at 5.5 kn gives ~0.005 HP = 4 W.

That is very likely way too little.

I also did a Savitsky method calculation using my own program. I have no idea about the parameters of your boat, but I quessed something and it gave 44 HP for the full scale. For the model scale it gave 14 W.

So for a very simple rule of thumb you 1:10 scale => 1:10000 power. Using Savitsky method I got something like 1:2300 power. Rick got 1:3100.

The latter two are clearly more accurate, since the simple formula does not take into account the clear change of Reynolds number, which leads to higher portion of friction drag at the model scale.

Bear in mind that planning boats are very sensitive to weight distribution.

Joakim

8. Guest625101138Previous Member

Joakim
I think your ratio of 2300 is better than my 3100. The prop would not be very efficient.

If you take 70% efficiency for say 50HP on the hull then full scale power is 71HP. Using your factor of 2300 the required model power is 23W. My feeling is that this would be close.

I have attached the MT Savitsky data for my approximation of the hull. The 50HP has a little allowance for windage. This is one factor that will not have much influence on the scale hull unless it is in a breeze.

rw - it looks like the 75HP would be close to the money. I doubt that a model will provide better power prediction than this but nothing like a model to get a feel for how a full size boat will behave in different sea conditions. Just building the model provides enlightenment.

Rick W

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rwatsonSenior Member

Very valuable info there Mr J - thank you for that.

You figures are veeeery spot on as well, because the previous version of this hull design got ~ 17 knots with a 50hp engine.

The realistic expectation for this newer design, with an increase in WL by ~1 metre , a 75hp instead of 50, with the similar weight should comfortably reach ~ 20 knots.

Rick - you data on gear weight is very usefull too - keeping the drive equipment light weight is a real priority.

I was very surprised by the great range of equipment available on the internet for model boats, and that was one site that I found.

My next big decision will be the prop sizes and gearing with the various electric motors. Range isnt so big an issue as I think 20 minutes of video will probably tell me as much as the model is going to.

If anyone has favourite radio gear, that is of interest to me as well. I will need more than rudder and speed servos, as it is a motor yacht, and fore and main sail trim controls will be required.

Great ideas everyone, many thanks.

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JoakimSenior Member

I should have been more clear, but the powers I mentioned for the Savitsky calculation already included the propeller efficiency (65%). They also include windage, whisker spray and appendage drag, but none of these are accurate without knowing details.

The main difference between my and your guess of Savitsky parameters is the beam. You used a very wide one. Try 3 m and you get much lower HP.

Joakim

Last edited: Apr 17, 2009
11. Joined: Aug 2007
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rwatsonSenior Member

Thats very usefull Joakim - because the actual boat has a maximum beam of 2.6 metres, so that was a great estimate.

One of the parameters of the hull design is that I am doing fairly rounded bilges to facilitate sailing, but I am aware that this will affect powered operation efficiency.

It will be interesting to see how the model behaves.

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If anyone is interested, the world speed record for model boats is held by an electric powered example. More than 100 MPH. I am often puzzled by the phenomenal performance of these little boats. They seem to violate a lot of the science that we believe in. Part of the departure from hydro dynamic rule is probably because the fast electrics touch the water only now and then. There is a web site, Fastelectrics.com, as a matter of fact.

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mwattsMartin

As a model flyer, I know a little about servo's.

You don't need a speed servo. These days most models use a BEC, which connects straight to your battery, provides 5 V to the receiver (which in turn provides the same 5V to the servo's), and provides variable power to the engine, giving you throttle control.

There are 2 main types of BEC. One for regular electric motors, and one for brushless motors. Brushless motors are a little more expensive, but provide more power in a lot smaller and lighter package.

There are databases available on the net that have been compiled by model enthousiasts, that can tell you exactly the thrust you can expect from a particular engine and prop combination. There are also some programs that can calculate this. So you should be able to create a setup that closely matches the calculated model power.

If weight is a problem, consider using LIPO batteries !: don't charge them with a NiCD charger! :!: ). They are lighter, provide more power, and can handle high discharges (a lot of amps).

As for servo's, the factors involved are pulling and holding force, weight and size. Larger servo's can pull harder and hold there position better under strain, but don't underestimate the potential of the small ones. You'll be surprised at the specifications. I think the smallest of servos could hold a (balanced) rudder for your model.

Furthermore, unless you like new toys, don't spend to much on a new transmitter / receiver set. Consider buying one from eBay. You don't need all the programmable electronics and trimmings that modern transmiters come with, so why pay for it. Second hand transmitter and receiver will work just as good.

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