Horsepower equation

[MTRiverDrifter]

I think I've seen this in an earlier post, but I can't find it.

Does anyone know a formula to calculate the speed of a hull given a different horsepower motor than one that is listed. For instance if a hull goes 50mph with 350 hp how much would it need to go 30.

Thanks

[mcdenny]

Planing boat speed varies with the square root of the weight divided by hp. From Gerr's Propellor Handbook: Speed in knots = C divided by sqrt(lbs/hp). C is is about 150 for regular runabouts.

[TR]

To use Crouch's Formula with any accuracy you need to know the weight of the boat, which is the lbs in the above posting. This is the weight (including fuel and people) at the time that your base speed was achieved.

If you know the base speed, power, and weight, you can calculate your own "C" constant to use in calculating new configurations. The accuracy of the constant depends on accurate input. And accuracy of the final calculation will depend on an accurate C, which is derived from the base boat's performance.


W is the weight of the boat in pounds.


MPH = C/(sqrt W/HP)

HP = W*(MPH/C)^2

C = MPH/(sqrt HP/W)

If your boat weighs 2000 pounds and goes 50 MPH with 350 HP, from the above we see C = 119.5

And so to feed 30 MPH and a constant of 119.5 into Mr. C's Formula we get HP = 126



Tad

[RonW]

Interesting and informative..
Seems to be base upon the square root of the hypothenose of the right angle divided by pie and multiplied or some such form of high mathimatical equation of .....

BUT- on the other hand for us less educated layman, Glen-l has a chart on their website that is amazing accurate or close enough for a city of this size.
The glory of it is, that it is simply based upon lbs per horsepower,
simple enough for planning hulls.
Hitting the highlights of the chart....

60 m.p.h. = 7 lbs per horse.
50 m.p.h. = 12 lbs per horse
40 m.p.h. = 20 lbs per horse
30 m.p.h. = 34 lbs per horse
25 m.p.h. = 46 lbs per horse

So it would seem that the 2,000 lb boat above would take 166 horses to run 50 m.p.h. and then would only take 59 horses to run 30 m.p.h.
Looking at riverdrifter's original post, at 350 horses and 50 m.p.h. it would seem that the boat weighed in at 4,200 lbs. gross..
And at that weight would only need 123 horses to go 30 m.p.h.

[TR]

Interesting curve Ron. My data shows most boats run faster than indicated by this curve, sometimes a great deal faster.

I hope you can see something of the data in the picture. W/HP runs along the bottom, speed in knots runs up the side. The dark curve is the Glen-L data. It seems really slow.

http://www.tadroberts.ca/pics/Powerweight.jpg

[John B]

Its almost as if Glen L didn't believe what the engine manufacturers claim for their horsepower.
Oh wait , thats right....:D

[RonW]

Interesting TR, very interesting. I take it that you have a lot of real life examples pegged out on the chart, thats good. Glen-l chart is on their website, use their search function on the main page as for speed chart and I think it will pop up. Good comparison
I have seen where most people say that after they built the boat, the chart was right on, but a few have said their boat was faster, lot of variables as always..
I believe as John says, that glen-l didn't buy the horse power ratings.
It does look as if glen's predictions are about 25% slower then yours, I have no answer other then plotting real examples.....

----Oh yea, that glen-l chart may be pretty old and slightly outdated, they maybe over the last 30 years or so the manufacturers are getting better performance at the props. better torque.?

[TR]

Ron,

The data points on the chart above are from tests by third parties or from my own designs. The upper edge curve is all large waterjet boats. In the highest speed group (upper left-hand corner) I note one outboard, one outdrive, and the rest are surface piercing drives.

The boats that fall very close on the Glen-L curve are a couple of small Bertrams (30 and 31), a Nelson 32 and 44 (semi-displacement) a Duffy 48, the Hinckley 39 Talaria, a couple of Hunt boats, and surprisingly, Tom Fexas's Midnight Lace44.

Yes, very very many variables. That is all I was trying to point out, one curve doesn't cover the range of possible performance. That is why it is so important to relate your C coefficient to boats of the same form and propulsion as your target.


All the best, Tad

[TR]

For instance the Glen-L curve postulates that this boat will run at slightly over 50 knots, and she actually runs at 62.

http://www.tadroberts.ca/pics/Rooster01.jpg

[Thomas Williamson]

Just for discussion purposes, my fiberglass flats boat (shallow V hull)at 14lb/ hp runs within 2mph of the Glen-L curve.

My Simmons Sea Skiff at around 28lb/hp (modified V hull) runs about 8 mph faster than the curve but ........at that speed the entire boat is out of the water except for the prop. The fastest speed where you could actually turn the boat safely agrees very well with the Glen-l curve.

Very intersting discussion. It seems pretty amazing that any of the curves could be anywhere close without taking into account the hull shape etc.

[RonW]

Hey Thomas, question, on your simmons that runs 8 m.p.h. faster then glen's chart, did you figure gross weight? People, gas, coolers with food and ice, fishing tackle, everything. After all the chart is based on gross weight, and for a small boat, people and other stuff can change that figure by 400 to 700lbs real quick.
That can put you on a different spot on the chart. Just curious.

On a side note, I have becomed very interested and going in the direction of the semi-planning/ semi-dissplacement hulls, what ever you want to call them. That run from the low teens to around 20 m.p.h. with william hand being credited, way back in the early 1900's, of his launches in the 30+ ft. range of achieving 22 m.p.h. with out planning, but still slicing and running smoothly through the water.
The figures I have so far are roughly -
70lbs per horse for 20m.p.h.
80 lbs per horse for 18m.p.h.
100lbs per horse for 15m.p.h.
200 lbs per horse for 12 m.p.h.

Here is where hull shape has a definite result.
Some of bill atkin mid teens, hulls seem to use less power, but I think he figured additional weight as people and so forth at a bare bone minimum.
Obviously to make the boat look very efficent.

On some of the planning hulls, when very little of the boat is even barely touching the water, what effect can the hull shape have on a speed factor, once the boat is out of the water??
Getting on top of the water is another deal.

[Thomas Williamson]

One person, no essentially no gear besides 6 gallon of gas with a 40 hp 4 stroke motor.

Thomas

[RonW]

Thomas is that weight already figured in? Or does the added weight change the equasion?

Just noticed the boat that TR posted that goes 62 instead of 50 has twin props, so what difference does twin props play in the equasion?

[mmd]

"...when very little of the boat is even barely touching the water, what effect can the hull shape have on a speed factor...?" - Thomas W.

Different hull shapes will have differing effects on the "speed factor" (I personally don't like usung generalizing factors in speed/horsepower predictions unless I am compelled to - there are too many variables that affect the answer to let a ham-handed "fudge factor" dictate the results.) For instance, a deep-vee hull will have greater wetted surface area than a shallow-vee hull. This will cause increased skin friction and require more horsepower to maintain a given speed, thus decreasing the lbs/hp for a given speed . That's the disadvantage of a vee-hull. The advantages are greater directional stability (the boat is less likely to suddenly want to point in another direction than the one it is travelling) and a softer ride (the hull slices through oncoming waves rather than slamming into them).

Crouch's Formula, stated by mcdenny and clarified by TR is by far the best required-power estimating method short of a full resistance analysis.

"...what difference does twin props play in the equasion?" - RonW

Propulsive efficiency - another fudge factor. General "guessequations" presume a certain propulsive efficiency, both mechanical efficiency of the drivetrain and hydrodynamic efficiency of the propeller, in their numbers. If you change the propulsive efficiency of the powerplant, you also change the presumed constant in the equation. Definitely a case of the closer you look at a simple problem, the more complex it becomes. That's why applying reams of data on similar boat types to derive a constant "C" as per TR's first posting is important - you try to use data gained from actual boats that are as similar to the boat in question to make the formula as accurate as possible. Anything else is just guesswork.

[MTRiverDrifter]

http://www.jespersenboats.com/html/rapture.htm

I'm still looking for the right boat to build next which has involved refining my understanding of my needs and desires. I've thought a lot about size and construction techniques and I'm now convinced I want something in the 22-26' range. I'd like to use solid wood and not ply. I'd like to run 25 to no more than 30 mph. A sedan cabin at the front with lots of room for fishing and family in aft cockpit is desirable. Economy running is important and If I can start with a plan by one of my favorite designers (Crocker, Garden, LFH) that would be a bonus.

Garden's rapture caught my eye as a potential starting place and the plans are avail at Mystic Seaport. The slight concave bottom should ride nice and the size is about right. I'd explore changing the stem profile and shear to give depth forward. I know it is a fast runabout, but I can see a mid speed sedan unlocked from the design with some FreeShip work. My question was to explore if the HP range slowed down (with out adding too much weight) would fit my desires. I also just wanted to know for other explorations in boat plans.

Rapture weighs 3080 lbs, has 350 HP and a 50 MPH advertised max speed.

[TR]

[quote=MTRiverDrifter]

Rapture weighs 3080 lbs [quote]

Note;
Rapture Displaces 3080 lbs, what she weighs we don't know. But I guarantee it's something different than her displacement. It might be close, or it might be a long way off, but we do not have any information about what she really weighs.

The displacement figure is a measure of the volume (usually in salt water) under the designed waterline. The weight is the actual total weight of every item that makes up the boat. It is always different (by some degree) than the displacement figure, which was a guess by the designer, made before she was built.


This is no reflection on either designer or builder, but the weight of any boat is constantly changing. Moisture levels in the wood change, paint and varnish levels change, junk comes and goes, people come and go, fuel comes and goes! All this changes the weight and thus the displacement every day.


Tad

[mcdenny]

Interesting, using Crouch's formula and a 150 constant 3080 lbs and 350 hp gives 50 knots, which is 57 mph.