Boat speed calculation

Hello everyone,

I need some help for calculating the speed for my boat. The drag for the hull is 136.3 N at 7 kts (8.055 mph). The driving power is 1kW and the rotational speed is 360 rpm.
Does anybody know the formula for calculating the boat speed?

It would be great if anybody could help me.

Thanks,

Alex

 

Are you a student? I will assume you are.

If the drag is 136.3 N at 7 kts then how what is the power which has to be applied to the hull to move it at 7 kts?

What is a reasonable assumption for the relationship between hull speed and the power acting to the hull?

Is the "driving power of 1kW" the power applied to the hull or the power applied to the propulsion system (propeller, water jet, paddle wheel, etc)?

If it is the power applied to the propulsion system then what is the efficiency of the propulsion system (power applied to the propulsion system / power acting on the hull)?

Answer those questions and you will be one step from the formula for calculating boat speed.

 

It is about reverse engineering the know facts.

Power = Total drag x Speed, or simply P = v.T

But the power has two different meanings. Either you are talking about the naked power Pn, or the delivered Power Pd. The above is simple the naked or EHP (Effective Horse Power) as it is also called too. The T is the thrust or in this case, drag.

Another way or writing this is the shaft horse power required ( Pd or SHP) is related to the efficiency of the whole system and the naked power (Pn or EHP). This is called the PC.

So the PC = EHP/Pd

But the PC is related to so many other variables, such as: appendages, hull shape, propulsion efficiency, efficiency of the prop behind the hull shape and efficiency in transmission.

However as a quick simple assumption you can use the PC = 0.5

So you can now rearrange the above to get the speed.

 

The value for the drag is from a hull drag test.

The propeller is for a pedal boat. There will be two people on the boat. For each person I calculated 500W.
The efficiency of the propulsion system is about 90-95%.
I used already JavaProp. Here’s the Screenshot

https://www.dropbox.com/s/ynvxivr1lneymtj/Screenshot JavaProp_E.jpg

Does anybody a good database for finding the right propeller?

Thanks

 

Drag varies with speed. The relationship between drag and speed needs to be known or assumed to rearrange the equations to get the speed corresponding to a given power.

 

More information is needed to approximate the relationship between drag and speed. How long is the boat? Displacment (weight in the water)? Beam? Hull shape?

Is this for a student project? If so what are you studying and what year are you in?

 

500W for how long? That is at the upper end of sustainable performance. FWIW most HPV props are custom to the application. Have you been to the IHPVA pages yet?

Also use the search feature with "human propeller"

http://www.boatdesign.net/forums/boat-design/propeller-power-human-6828.html

http://www.boatdesign.net/forums/boat-design/pedal-powered-boats-23345.html

 

Correct.
He only provided an absolute, not a range. Thus confused what you're suggesting?

I'll repeat again for the hard of reading:

 

The original poster provided the drag at a single speed, 136.3 N at 7 kts (8.055 mph) which is 3.60 m/s. A drag of 136.3 N at 7 kts yields an EHP of 491 watts.

He also stated that "The driving power is 1kW and the rotational speed is 360 rpm." and asked for "the formula for calculating the boat speed".

In order to determine the formula for speed as a function of power, either EHP/pn or SHP/pd, the relationship between speed and drag needs to be known. Drag varies with speed. The formula for speed as function of SHP/pd also needs the value of PC which as Ad Hoc correctly noted "is related to so many other variables, such as: appendages, hull shape, propulsion efficiency, efficiency of the prop behind the hull shape and efficiency in transmission."

Unfortunately the original poster only provided a single point of the drag vs speed relationship. That point is only sufficient if EHP is close to 491 watts or the combination of SHP and PC is such that the EHP is close to 491 watts. The original poster states the driving power is 1kW. If this is the SHP then Ad Hoc's suggestion to use a PC of 0.5 with a resulting EHP of 500 watts suggest that the resulting speed will be 7 knots. Otherwise additional information or assumptions are needed to expand that single point to the drag vs speed relationship over the required to solve the equations which Ad Hoc gave in post #3 to obtain the speed when the "driving power is 1kW".

The image from JavaProp in post #4 by the original poster shows an efficiency of 83% which suggests a PC greater than 0.5. Also in the same post is the statement that "The efficiency of the propulsion system is about 90-95%." This suggests that for an input power at the pedals of 1kW the SHP at the propeller will be 900 watts to 950 watts.

 

Correct, ergo only one pint for discussion.

With only one point that is all one can do, provide one answer; limited, comprehensive, incorrect or otherwise.

I am frequently asked by clients what will be the speed of my boat, but only provide a single data point, or sometimes none at all.

All one can do, is provide an answer based upon the single data point and no more. Anything else is pure speculation and supposition. If the client, or poster in this case, only provides basic rudimentary data, then the reply can only be consist with such. If they are unable to provide further data whose fault is that? It doesn't alter the procedure - only the fudge factors one uses to arrive at an answer, correct or otherwise.

 

But there's more! Did the hull drag test allow/correct for windage of 2 people? Efficiency of 90% seems high, if it includes everything. Maybe just the drive train would be possible at 90%+ ?

Just my 2 cents, FWIW.

Porta

 

I can see from the discussion that it is not as simple as I thought. So therefore I should trial and error. Thank you.

Just for information here is a screenshot from the drag / speed relationship. (x-axis=speed; y-axis=drag)

https://www.dropbox.com/s/lhn5swqayhw3n9d/Drag.jpg

 

P=FV
again this gives you only single point. but at least you can calculate the power needed for your test speeds.

for example

V=8kts = 4.12m/s
F=176.9N

P=728W

so if you add inefficiencies of the drive-train and propeller (no way combined are 95% efficient) and added drag of appendices not on the boat during the tow test you are pretty close to the point where 1000W on the pedal cranks gives you 8 knots. It might get to 8.3 knots or something but the resistance curve (even if it stayed linear) is already pretty steep.

 

Where are you getting values of 90-95% efficient? They are not realistic.

 

If you will be using a GPS for your trial and error, be prepared for big windage errors on open water, or with non apparent currents.

Porta