That's a great explanation Wilson. As moderator, I added the "root" to your 1st sentence to correct the relationship you were intending. But something bothered me a little bit with this still. In your 2nd paragraph, you correctly show that delivered FORCE is proportional to the square of the ratios of the speeds. But Force is not Power, so the first paragraph doesn't go far enough as I see it.
Let's look at the simplified physics a bit:
· Power = Force * Speed
· Work = Power * Time = Energy expended
· Distance = Speed * Time
Since we accept that the Force ratio is proportional to the square of the speed ratios [ F1/F2 = k * (v1/v2)^2 ], then since Power = Force * Speed, then:
· P1/P2 = k *(v1/v2)^3
So your first paragraph statement of a square relationship between the power and speed doesn't go far enough. It's actually a cubic proportion, which amplifies the effect you describe even further (in terms of power, not force). If you look at windmills also, it's known that the power available by the wind is proportional to the cube of the wind speed, not the square. Force is proportional to the square of the speed.
Interestingly, if we look instead at the ratio of ENERGY per DISTANCE, the FORCE and SQUARE effect applies:
· Energy / Distance = (Power * time) / (Speed * time) = Power/Speed = Force = k * v^2
So, looking back at the numbers you provided, the ENERGY expended for a given distance travelled at those speeds applies, but in terms of POWER, you need to turn each of those ratios into a CUBE.
In case this helps-
-Myles Twete, Portland, Or.
From: electricboats@yahoogroups.com [mailto:electricboats@yahoogroups.com] On Behalf Of Wilson Frye
Sent: Thursday, March 10, 2011 9:37 AM
To: electricboats@yahoogroups.com
Subject: Re: [Electric Boats] Thrust to speed numbers
The best rule of thumb I have seen or used in over 40 years of hanging around displacement boats with a centrifugal propellor is that the speed of a boat will be approximately proportional to the square [root] of the input power until hull speed is reached.
James Cat 30's hull speed is a bit less than 7 knots. In his lab experiment (pull test), at speeds less than hull speed, he measured the thrusts his prop would need to provide to push his boat. If you ratio his speeds to his initial speed of 2 knots, the ratios are 3/2 (1.5), 4/2(2), 5/2 (2.5), and 6/2(3). The squares of those ratios are 2.25, 4, 6.25, and 9. The squares of those ratios times the 2 knot thrust of 20 pounds are 45, 80, 125, and 180. These numbers compare favorably to James' experimental findings: 35 vs 45, 60 vs 80, 100 vs 125, and 180 vs 180.
This relationship between input power and speed allows you to quickly evaluate how changes in power applied will affect speed. Especially useful is the knowledge that if you halve the power, you retain seventy percent of your speed. And it follows that if you halve it again to 25 percent of the original power, you retain 70 percent of that 70 percent speed, which is about half the original speed.
On Mar 10, 2011, at 4:11 AM, GNHBus@aol.com wrote:
You hit the nail on the head with "watts - to - knots - to - rpm" It is very interesting when you start looking at the Power Curves between
diesel vs. electric propulsion, as the interest steers toward the propeller for achieving hull speed.
-----Original Message-----
From: Eric <ewdysar@yahoo.com>
To: electricboats@yahoogroups.com
Sent: Wed, Mar 9, 2011 6:24 pm
Subject: Re: [Electric Boats] Thrust to speed numbers
GNHBus,
I don't know if you tried to attach something to your post, but I don't get attachments for Yahoo group posts.
James' measured data shows 20 pounds of pull for 2kts, 35 pounds of pull for 3kts, 60 pounds of pull for 4kts, 100 pounds of pull for 5kts and 180 pounds of pull for 6kts with his Catalina 30 in Santa Barbara harbor. The basic presumption is that if you're not being towed by another boat, the prop (or sails) has to provide an equal amount of thrust to achieve the same speed.
This data shows the exponential type of power requirement that I am familiar with in boats. In James' data, it takes about 3 times the force to drive the boat 2kts faster. This will simple conversion rule will come apart as the boat approaches hull speed, but it seems to work from 2kts through 6kts. You should see curves with a similar shape with observed data from other boats.
But when you look at the electricity required to produce that thrust, the curve gets steeper. Again looking at James' data, the rule is closer to doubling the power to gain 1kt. It is my belief that this is at least partially related to increased prop slip as the loads get higher. I plan on collecting detailed data (watts to knots to RPM) for my boat, but the weather hasn't been cooperating each time I've been at the boat for more than the last month.
Fair winds,
Eric
Marina del Rey, CA
--- In electricboats@yahoogroups.com, GNHBus@... wrote:
>
> This indicates 50ft/lbs/sec Prop Thrust for 4knots, and 100ft/lbs/sec Prop
> Thrust for 6knots
> for Catalina 30 at 10,200lbs, through Sea Water, is that about right ?
>
>
> In a message dated 3/9/2011 12:55:25 P.M. Eastern Standard Time,
> ewdysar@... writes:
>
>
>
>
> GNHBus,
>
> I know that you've seen the link posted here before. James Lambden at
> Propulsion marine has collected extensive data concerning his Catalina 30
> Kapowai and posted that data online at _http://electricboatdesign.com/_
> (http://electricboatdesign.com/) . If you look in the "data" tab, James has posted
> thrust requirements based on measuring the pull while towing his boat. In
> that table, 100 lbs of pull (thrust) occurs at 5kts. Keep in mind that this
> is empirical data, not theoretical like the results from the various
> planning worksheets....
> Fair winds,
> Eric
> Marina del Rey, CA
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