Scaling power?

[Saqa]

Hi all
I intend to scale down a 30' hull to 3' for testing bottom shape. How do I scale 120hp down to suit? I want to pick up RC hardware including electric motor, rudder control, throttle control

Inboard setup

Thanks

 

[Ad Hoc]

With all things being equal, for the scaling (geosim) it is the ratio of the scale to the power 3.5

 

[fredrosse]

I hope you intended to scale a 30 foot hull down to a 3 foot model, rather than a 3 inch model?

 

[Saqa]

I hope you intended to scale a 30 foot hull down to a 3 foot model, rather than a 3 inch model?

Sorry, corrected

 

[Saqa]

With all things being equal, for the scaling (geosim) it is the ratio of the scale to the power 3.5

Ad Hoc, I am good with my hands but not a mathematician. Could you please expand a bit more? Is my size ratio 10:1? Does "to the power" mean 10:1 x 10:1 x 10:1 x (10:1/2)?

Sorry, I really do not know how to multiply a ratio. Someone please help!

 

[Ad Hoc]

Lengths = 3/30 = 1/10
That's your ratio scale factor.

EHP = 120hp x (1/10)^3.5 = 120 x 0.000316 = 0.0378 or 0.04Hp

At the correct scale of speed too.

 

[fredrosse]

For a displacement type hull, at hull speed or less the propulsive power needed is directly proportional to the hull displacement, at equal speed/length ratios.

Max Hull speed (knots) = 1.3 * squareroot of waterline length (feet)

Speed-Length Ratio = Speed / squareroot Length

So, if your waterline length is 28 feet, the nominal maximum hull speed is 6.9 knots.
If your model is 1/10 scale, then its hull speed is 1.3 * squareroot 2.8 which is 2.18 knots to mimic the big boat performance.

Displacement scales as a cubic function, so the 1/10 scale model has a displacement of 1/10 * 1/10 * 1/10 = 1/1000 of the big boat.

The result is that, with the model going at max hull speed (2.18 knots), it will require propulsive power of 120HP/1000 = 0.12 HP, or 90 watts, assuming equal propulsive efficiency for both the big boat and the model. This condition of the model mimics the big boat that requires 120 HP to make 6.9 knots, equal speed-length ratio for both the big boat and the model.

These numbers are for displacement type hulls, for planing type boats the functions are different.

 

[Saqa]

Lengths = 3/30 = 1/10
That's your ratio scale factor.

EHP = 120hp x (1/10)^3.5 = 120 x 0.000316 = 0.0378 or 0.04Hp

At the correct scale of speed too.

Thank you, really appreciate the quick response and help. And for future use could you please teach me what this means
= 0.0378, lets call this x

If I want to scale another HP powerplant, you have shown how to arrive at x. What do I need to do to x to arrive at HP?

Fredrosse
Thank you. Noted for future use. This model will be planing

 

[Ad Hoc]

.... for future use could you please teach me what this means
= 0.0378, lets call this x

It is the answer to the sum

EHP = 120hp x (1/10)^3.5 = 120 x 0.000316 = 0.0378 or 0.04Hp

 

[Saqa]

It is the answer to the sum

Sorry, I still don't understand how 0.0378 converts to 0.04Hp

 

[Saqa]

30w electric motor

Available in a local shop. They also have some props and things. Lots of options online to play with. I think 8yr old daughter will love these experiments. We have a two-hour playtime every afternoon after school, and this model testing will be an excellent project for us. They will be doing RC and programming in school too. She loves making things too

 

[Ad Hoc]

Sorry, I still don't understand how 0.0378 converts to 0.04Hp

It is called rounding up to the nearest/closest number - rather than using lots of numbers.

0.038 if i times this by 1000 = 38.
0.040 if i times this by 1000 = 40.

Whenever you ask some one how long will you be... most would say 5mins or 10mins... rarely would you hear i will be 6.35mins or something like that.
It is called rounding up or rounding down, to the nearest number for simplicity.

 

[Saqa]

It is called rounding up to the nearest/closest number - rather than using lots of numbers.

0.038 if i times this by 1000 = 38.
0.040 if i times this by 1000 = 40.

Whenever you ask some one how long will you be... most would say 5mins or 10mins... rarely would you hear i will be 6.35mins or something like that.
It is called rounding up or rounding down, to the nearest number for simplicity.

Thanks, didn't realise you were rounding off. Makes sense, thanks heaps

 

[Saqa]

Planing hull

So size scale is 1/10

Power scale
EHP = 120hp x (1/10)^3.5 = 120 x 0.000316 = 0.0378 or 0.04Hp

Weight
1/(10*10*10) = engine 200kg/1000 = 200g

They don't list motor weight but whatever it is, do I add ballast around it to bring the total in that engine bay to 200g?

Is this correct?

 

[fredrosse]

The displacement of the model needs to be 1/1000 of the displacement of the big boat. That is a boundary condition that needs to be met for modeling purposes. The 1/10 scale model needs to float at the same (scale) hull draft as the big boat. If the big boat has a draft of 2 feet, then the model needs to have a draft of 0.2 feet. With that condition the model will displace 1/1000 of the big boat displacement. This total displacement weight is for the entire boat, it does not matter if the drive motor has a different scale weight than the big boat engine, what matters is total displacement weight.

The other item that needs to be addressed is model speed vs big boat speed. For a displacement type hull, this is the speed-length ratio, described in my earlier post. For a planing type hull the proper scaling factor for speed I do not know. Ad Hoc mentions this also, perhaps someone can elaborate on scale speed of planing hulls?