Power-weight-speed scaling law

Optimizing the performance of Boston Whaler boats
sandhammaren05
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Power-weight-speed scaling law

Postby sandhammaren05 » Sun Jan 20, 2019 7:01 am

Older threads mention Crouch's formula. Crouch's formula is wrong, it cannot be derived from hydrodynamics.

Specifically, the 'constant' (fudge factor) in the formula is not dimensionless, it has units. A correct scaling law is free of dimensions. I have derived a 1/3 power law for power-weight-speed scaling from hydrodynamic scaling of propeller efficiency. There is no fudge factor, there is only scaling, where boats and engines are divided into different classes by the drag coefficients of the gearcase and boat bottom. The scaling law has been checked and is in agreement with existing APBA OPC kilo records.

The Boston whaler is a Hickman Sea Sled design and that's pretty much the only Sea Sled produced today. So Whalers can be compared with Whalers using the formula. An earlier Sea Sled was the 1965 Carlson Contender.

Here's the link to my paper, where the scaling law for propeller diameter is also presented and compared with APBA OPC kilo records

http://arxiv.org/abs/1602.00900

I'm writing a book manuscript about the hydrodynamics of surface piercing propellers and fast boats. The discussion will be included there in expanded form.

jimh
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Re: Power-weight-speed scaling law

Postby jimh » Sun Jan 20, 2019 2:12 pm

sandhammaren05 wrote:Crouch's formula is wrong...


Crouch's formula, as you yourself mention, is an empirical relationship between boat speed and power-to-weight ratio. It works with reasonable accuracy.

In order to dismiss its use, I would need a similar method to predict boat speed based on:

--power
--weight
--hull shape

If your treatise offers such a formula, please post it here. I would then like to test it to see if your method delivers predicted boat speed with the same accuracy as Crouch's method does when the well-know hull factor of 180 for a Boston Whaler moderate V-hull shape is used.

jimh
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Re: Power-weight-speed scaling law

Postby jimh » Sun Jan 20, 2019 2:16 pm

sandhammaren05 wrote:...The Boston [W]haler is a Hickman Sea Sled design and that's pretty much the only Sea Sled produced today. So Whalers can be compared with Whalers using the formula.


Only the very early Boston Whaler hulls with prominent twin runners were similar to the Hickman Sea Sled. The more modern Boston Whaler hulls, say since the introduction of the V-20 OUTRAGE in the c.1980, are moderate V-hulls with a relatively constant deadrise, and the runners are now much reduced in size. I doubt that speed estimates for these modern hulls could be done using the Hickman Sea Sled as a basis for modeling the hull, but, if you have data that shows otherwise, you should not be shy about presenting it.

sandhammaren05
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Re: Power-weight-speed scaling law

Postby sandhammaren05 » Tue Jan 22, 2019 3:33 am

You miss the point. The Sea Sled defines a class. V-bottoms define a different class. Pad V [silly expression deleted], tunnels another.

The boats compared need only have he same drag coefficient.

sandhammaren05
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Re: Power-weight-speed scaling law

Postby sandhammaren05 » Tue Jan 22, 2019 3:36 am

Crouch's formula is not empirical, it cannot be obtained by plotting empirical data. Crouch's formula is a stab in the dark, nothing more. The best way to check his scaling law against data is to plot

U/(p/w)^1/2.

If the formula is correct then you will get a straight line with scatter. You can do the same with my 1/3 power
scaling law, but if you look at the closeness with which it reproduces the APBA OPC kilo records then you likely will not bother. Thanks again for the pm with corrections.

sandhammaren05
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Re: Power-weight-speed scaling law

Postby sandhammaren05 » Tue Jan 22, 2019 7:52 am

jimh wrote:
sandhammaren05 wrote:Crouch's formula is wrong...


Crouch's formula, as you yourself mention, is an empirical relationship between boat speed and power-to-weight ratio. It works with reasonable accuracy.

In order to dismiss its use, I would need a similar method to predict boat speed based on:

--power
--weight
--hull shape

If your treatise offers such a formula, please post it here. I would then like to test it to see if your method delivers predicted boat speed with the same accuracy as Crouch's method does when the well-know hull factor of 180 for a Boston Whaler moderate V-hull shape is used.



Thanks to jimh various typos in the ms have been corrected, but it will take time before the corrections will be made where the paper is archived. I can send a corrected copy of the ms to anyone who sends me a pm with email address. The file is too large to attach here. I also have a paper on lift onset and planing, including an empirically correct lift coefficient for v-bottoms.

jimh
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Re: Power-weight-speed scaling law

Postby jimh » Tue Jan 22, 2019 9:25 am

What information about my boat do you need to predict its speed?

I can tell you:

Engine shaft horsepower = 225-HP
Propeller pitch = 17
Total boat weight = 4400-lbs

What other data do you need to predict the boat speed in MPH?

sandhammaren05
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Re: Power-weight-speed scaling law

Postby sandhammaren05 » Tue Jan 22, 2019 12:56 pm

jimh wrote:What information about my boat do you need to predict its speed?

I can tell you:

Engine shaft horsepower = 225-HP
Propeller pitch = 17
Total boat weight = 4400-lbs

What other data do you need to predict the boat speed in MPH?


I have a scaling law. You'd need data for another rig in the same class of drag coefficient. To make an absolute speed
prediction you'd also need the drag coefficient and prop efficiency, neither of which is generally available due to too little (and also unreliable) data.

With the scaling law you can answer questions like: (i) if I repower with different hp then what percentage speed gain can I expect?

(ii) If I add weight to my present rig how much
will be the speed loss?

jimh
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Re: Power-weight-speed scaling law

Postby jimh » Tue Jan 22, 2019 1:31 pm

sandhammaren05 wrote:With the scaling law you can answer questions like: (i) if I repower with different hp
then what % speed gain can I expect? (ii) If I add weight to my present rig how much
will be the speed loss?


Can we try your method with data from my boat? Here is some data; and let me know if you need more data.

Total boat weight = 4400-lbs (based on some actual scale measurements with the boat on the trailer, then subtracting out the trailer weight)
Horsepower =225 (based on EPA emission sticker rating)
Boat speed = 42-MPH (measured with GPS with WAAS augmented precision)

How fast can you predict my boat to go if I increase to 300-HP? Assume the weight remains constant.

sandhammaren05
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Re: Power-weight-speed scaling law

Postby sandhammaren05 » Wed Jan 23, 2019 3:27 am

The 300 weighs more than the 225 and you didn't tell me the weight. Were the motors to weight the same then the speed gain would be 10%, you would expect to gain a little over 4-MPH.

% speed gain=(P2w1/P1w2)^1/3

jimh
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Re: Power-weight-speed scaling law

Postby jimh » Wed Jan 23, 2019 11:18 am

Assuming the weight is the same, that is, w1=w2, then your method for speed prediction is

Speed ratio = (P2/P1)^0.33

In the instant case, speed was 42-MPH, so the predicted speed would be 42 x (300/225)^0.33 = 42 x 1.099 = 46-MPH.

Crouch's method would estimate 42 x (300/225)^0.5 = 42 x 1.155 = 48.5-MPH

Yellowjacket
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Re: Power-weight-speed scaling law

Postby Yellowjacket » Fri Jan 25, 2019 10:20 pm

Crouch's approach works fine for a limited speed range and for hulls that are not operating at high speeds. It assumes a prismatic hull and no significant changes in setup. Since it does not consider aerodynamic lift or drag it's not going to accurately predict behavior where those aspects become a major driver in performance as is the case with race boats. Within those limitations, it provides a decent "rule of thumb" as to what to expect from a power change for a planing hull at moderate speeds.

Savitsky's analysis is more analytical, but it is also based highly on empirical obeservations, but given a prismatic hull and reasonable speeds it does give fairly good results.

Crouch's formula and Savitsky's analysis both fall apart at high speeds, and very low trim angles where air starts to become entrapped under the hull for a significant portion of the hull, as is the case with APBA outboard classes where very light hulls running at high speeds are essentially riding on the tips of the ripples. Similarly, the very high speed padded hulls will start to exhibit the same behaviour and drag drops significantly compared to predictions at really high speeds.

The original Whaler is a poor candidate for analysis by Crouches formula unless you're looking at a very narrow speed range. The problem is that the hull has significant hook at the transom. At low speeds the hook provides the ability to plane with lower power which would give you a Crouch's coefficient that isn't applicable at higher speeds. At moderate speeds the hull is efficient and trims reasonably, but as speed increases because of the high stern lift present, the hull trims nose down and wetted area increases, which is exactly opposite of what happens on a conventional prismatic hull that is trimmed correctly and has the center of gravity optimized for each speed. For the later series boats, Crouch's formula will provide decent results, again assuming the speeds are not so high that aerodynamics become predominant, or that the hul starts to "break out" as is the case with very fast or racing boats.

sandhammaren05
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Re: Power-weight-speed scaling law

Postby sandhammaren05 » Sat Jan 26, 2019 5:18 am

Sandwiched response:

Crouch's approach works fine for a limited speed range and for hulls that are not operating at high speeds. It assumes a prismatic hull and no significant changes in setup. Since it does not consider aerodynamic lift or drag it's not going to accurately predict behavior where those aspects become a major driver in performance as is the case with race boats. Within those limitations, it provides a decent "rule of thumb" as to what to expect from a power change for a planing hull at moderate speeds.

Why use a faulty rule of thumb when the correct scaling law is available? Is it a problem for you to take a cube root rather than a square root? Aerodynamic lift and drag are not important at low speeds, throwing that in is a red herring. As I pointed out, if you plot U/(p/w)^1/2 you will not be able to identify scatter about a constant. The foru=mul a is wrong, period.


Savitsky's analysis is more analytical, but it is also based highly on empirical obeservations, but given a prismatic hull and reasonable speeds it does give fairly good results.


There is no analysis in Savitsky, it's all hand waving. He firmed up nothing but did muddy the waters.



Crouch's formula and Savitsky's analysis both fall apart at high speeds, and very low trim angles where air starts to become entrapped under the hull for a significant portion of the hull, as is the case with APBA outboard classes where very light hulls running at high speeds are essentially riding on the tips of the ripples. Similarly, the very high speed padded hulls will start to exhibit the same behaviour and drag drops significantly compared to predictions at really high speeds.

High speeds has nothing to do with the failure. If you plot U/(P/w)^1/2 at low speedds then you will not get a constant. Try it. Crouch and Savitsky fall apart at all speeds. My scaling law works extremely well comparing a 1956 15' Feather Craft/1960 Scott 40 against a 1948 10.5' Feather Craft/1957 Evinrude 18. Crouch and Savitsky cannot predict the right scaling at those low speeds (27-33 mph).

The original Whaler is a poor candidate for analysis by Crouches formula unless you're looking at a very narrow speed range. The problem is that the hull has significant hook at the transom. At low speeds the hook provides the ability to plane with lower power which would give you a Crouch's coefficient that isn't applicable at higher speeds. At moderate speeds the hull is efficient and trims reasonably, but as speed increases because of the high stern lift present, the hull trims nose down and wetted area increases, which is exactly opposite of what happens on a conventional prismatic hull that is trimmed correctly and has the center of gravity optimized for each speed. For the later series boats, Crouch's formula will provide decent results, again assuming the speeds are not so high that aerodynamics become predominant, or that the hul starts to "break out" as is the case with very fast or racing boats

A hook causes poor performance in any case, but my scaling law will work for the Whaler. Try my predictions for repowering a Whaler.