You would think that if every paddler could produce the same amount of power, then 20 paddlers would provide 20 times more power than one paddler. Right?

Yes, you are right.

You would also think that 20 paddlers should be able to make the boat go 20 times faster than one paddler in the same dragon boat. Right?

Wrong!!!

Why?

Water is to blame. Water resists things moving through it, including boats. The faster you move the more it resists – the more power you have to provide.

It all pivots around the drag formula:

The formula below will show you that the Power requirements go up as the cube of the speed (velocity).

__FORMULAS__

__FORMULAS__

Given the following:

p = fluid density (salt water, fresh water, hot water, cold water, air, oil, etc.)

C = drag coefficient (how streamlined the boat hull)

A = cross sectional area (the area of boat hull pushing through the water)

v = relative velocity (difference between the speed of the boat and the water)

k = (½ x C x p x A). The shape of the boat and the water characteristics stay the same, they equate to a certain number (a constant). And I will assume the constant is 1. That way the answer is a Power Factor rather than the actual power.

**Drag** = ½ x C x p x A x **v ^{2}**

**Power ^{ }**= Force x v

and since Drag is a force

**Power **= Drag x v

**Power **= (½ x C x p x A x **v ^{2}**) x v

= (½ x C x p x A) x **v ^{3}**

** ^{ }**= k x

**v**

^{3}**Power Factor **= **v ^{3}**

The Power Factor simply shows the overall relationship between Power and Velocity.

## Example

Suppose one paddler, George, has enough power to move the boat by himself at 5 km/hr.

The power required to do that depends on a whole bunch of things including the shape and texture of the boat, the type of water (salt, fresh, hot, cold), and the speed.

All of these variables affect the drag experienced by the boat. And it is the paddling power required to match this drag that limits the speed of the boat. The kicker, as we have seen, is that the power required to work against this drag is proportional to the speed CUBED. Yes cubed!

So in this case, for George, to move the boat at 5 km/hr requires a *power factor*^{*} of 5^{3} = 125. (Power is proportional to velocity cubed)

The *power factor* required to **double** the speed (2 x 5 = 10km/hr) is (2×5)^{3 }= 1000 = **8** x 125

8 times more power to go 2 times the speed. Ouch!

Put another way (if all the paddlers had the same power as George):

**1**paddler with a Power Factor of 125 could move a boat at 5km/hr- We would need
**8**paddlers with a combined Power Factor of 1000 in order to go 10km/hr (2 times faster). - We would need
**27**paddlers with a combined Power Factor of 3375 to go 15km/hr (3 times faster) - To go 20 times faster (100km/hr), we would need
**8000**paddlers like George!! Ridiculous I know.

## How Fast Can the 20s Boat Go?

OK, so a 20 paddlers cannot go 20 times as fast as one paddler.

So how fast **CAN** the boat go with 20 paddlers each with the same power as George?

…. The remainder of this content is for members only…

Ya sabemos que 1 palista genera una velocidad de 5km/h y una fuerza de 125 kwh

Durante cuanto tiempo testeo al palista para que llegue a esos 5 km/h??

Si 20 palistas generan una potencia de 2.500 kwth… como se que velocidad van a alcanzar??

Hi Nicholas,

I translated your questions into English to answer them.

Question 1: How long do I test the paddler to reach those 5 km / h?

Answer: What I have done with a crew is get them all to stop paddling except for one. That one paddler then paddles for about 50 strokes and I measure their speed. Some paddlers can get the boat to 7 km/hr while others can only get to 4 km/hr. For the post I selected 5 km/hr as an example. The reason I do it with the crew in the boat is to keep as many of the other variables constant (e.g. the amount of hull in the water)

Question 2: If 20 paddlers generate a power of 2,500 kwth … how do I know what speed they will reach?

Answer: Firstly let’s be careful with the units. There is a formula that links power and velocity in a fluid. It has many variables which I bundled up and assumed a value of 1 to make the post simpler. What I am left with is a “relationship” between power and velocity which I have called a power factor (It is a number. It is not watts). This relationship says that the power factor is proportional to velocity cubed or velocity is proportional to the cube root of power factor.

So if the power factor for one paddler is 125 and we have 20 identical paddlers, then the power factor for 20 paddlers will be 20 x 125 which is 2500. And I know that the speed they reach will be proportional to the cube root of this power factor which is about 13.6 km/hr. I do not know the actual power in watts of the one paddler or the 20 paddlers but if all other variables are kept constant then the relationship between power and velocity will hold true for the power factor.

I hope that answered your questions.