Formula for Calculating Speed

[10gauge]

Here's a mathematical formula I derived to calculate speed (mph) for a cat only.

Basically, it gives you an average figure for speed, based on a collection of 30 actual catamaran setups I've come across online. It takes into account the prop, kv, volts, rpm. This formula works for LiPo power only. Engineers relax, I am only a dentist. Differences in prop slippage, friction losses, cat hull design, weight, electrical/mechanical issues are all moot since this is not a theoretical equation. This is a statistical equation based on samples under their actual running conditions.

mph = [Prop Factor] x [Prop dia] x [kv motor] x [LiPo Volts] x 0.000687

or

mph = [Prop Pitch] x [Prop dia] x [Prop RPM] x 0.000687


or

mph = [Prop Distance per Revolution] x [kv motor] x [LiPo Volts] x 0.000687

Remember it's only a statistical approximation for speed. As they say, individual results may vary. Good Luck!

[ReddyWatts]

Is this a metric or standard formula? My calculation did not come out right. Maybe give us an example with real numbers?

[Diegoboy]

Where does the weight of the boat plug in this equation?

[ReddyWatts]

FE is changing, I wish Fe Calc would also calculate these components into the equation:

Number of motor poles and 1p or 2p lipo's.

1. 2-pole stator of 80-mm diameter and 90-mm length will output around 1.7 Nm torque; a 4-pole motor will output 2.3 N-m torque. A 6-pole motor in the same size would have about 2.8 N-m torque.

2. Battery resistance changes when you parallel them.

Fe Calc automatically adds n the weight of the batteries, motor and drag for each hull type, but it is really becoming a complex equation to calculate FE setups.

[10gauge]

Remember this is not an equation based on electromechanics. It is a statistical equation based on averaging many samples I've come across online, including setups on this site. It will not work on every set up, but I found the result is quite close on most setups, and more importantly it gives you a quick and easy value before you take your setup to the lake.

The information used in deriving the equation takes into account the prop, kv rating, and LiPo volts. In other words, it doesn't take into account number of poles, motor efficiency, torque differences, prop position, weight, LiPo output and quality, hull slip factor, electrical resistance, frictional losses, hull size, etc.... It's a simple and quick way of getting a real world approximation based on the average of real setups with actual speeds.

ReddyWatts, I need to clarify what I mean by prop pitch, because Jay Turner was initially getting an incorrect calculation as well. But after I clarified one of the terms in the formula on RRR, He said I was very close to his own formula. In fact we were within 3% of our calculated values.

The prop pitch is the prop factor, i.e. 1.4x, 1.5x, or 1.6x for octura props. The prop diameter is in inches. The coefficient of 0.000687 is derived from 30 different setups and it's calculated to give you mph when you plug it into the formula. Here is the same formula with better clarification.

mph = [Prop Factor] x [Prop dia] x [kv motor] x [LiPo Volts] x 0.000687

or

mph = [Total Prop Distance per RPM] x [kv motor] x [LiPo Volts] x 0.000687


Remember: the equation is ONLY for LiPo and Cat designs. It's only a starting point, I guess you could modify the equation to reflect different hull types and account for their hull slip factors. Jay Turner said 75% for Cats and 80-85% for Hydros.

Here are some actual examples of mostly M-1 SuperCats and Mean Machines:

Setup 1: Lehner 2250/11, 8S, x447, claimed speed 60mph
1.4 x 1.85 x 1076 x 29.6 x 0.000687 = 57mph calculated speed

Setup 2: (Jay Turner) Neu 1521/1D, 4S2P/3300/25C, m440, claimed speed 62mph
1.4 x 1.57 x 2800 x 14.8 x 0.000687 = 63mph calculated speed

Setup 3: Feigao 12XL, 6S2P/8000, Y537/3, claimed speed 48.6mph
1.5 x 1.46 x 1390 x 22.2 x 0.000687 = 46mph calculated speed

Setup 4: Lehner 2240/7, 6S, x445, claimed speed 70mph
1.4 x 1.77 x 2114 x 22.2 x 0.000687 = 80mph calculated speed

Setup 5: Feigao 8XL, 4S/6400, x640, claimed speed 50mph+
1.6 x 1.57 x 2084 x 14.8 x 0.000687 = 53mph calculated speed

[ReddyWatts]

Thanks 10Gauge. It works now! Pretty close too!

[Eodman]

So Ten guage if I have a toysport twin drive do I do the equation then multiply by two? Just asking!!!!

[10gauge]

Eodman, by having twin drives, it will be faster, but I don't think there will be a linear increase of doubling speed. Regardless of the number of drives, you can't exceed the theoretical distance traveled by a prop for a given rpm, regardless of how many there are working in tandem. Sure you're displacing twice the volume of water, but the velocity of water remains constant. Some may also argue that prop area may have little to do with speed, as long as the prop is not too small.

Doubling the prop area ensures less prop slippage by increasing the prop transfer function closer to the theoretical value of 1.0:1. In other words, with 2 props at a constant rpm, the actual distance of the spinning prop should approach the theoretical distance than would a 1 prop setup.
Ideally, the prop slippage should decrease by 2, so instead of 0.75 slippage for a cat, half the distance to 1.0 would be 0.125.

(1.0 - 0.75)/2 = 0.125

Then 0.75 + 0.125 = 0.875 new slip factor for 2 drives.

I am assuming a slip factor of 0.75 for a cat. With 2 drives the new slip factor is 0.875, a 17% increase in speed.

so just multiply the speed in the original formula by 1.17 to get the new speed.

Of course I've ommited any discussion of additional weight, fluid dynamics, etc.

On an aside, based on what I am assuming about prop/hull slip factors, it would seem a twin drive would yield less gain in speed for hydros, than it would for monos?? I am not sure, I'll have to ponder this one.

[Eodman]

Bumped for new member

[10gauge]

It's been 2 years since I derived this statistical approximation for calculating speed. In another thread, Jay Turner and I discussed the validity of this formula and he compared it with his own formula. Remarkably, our formulas for calculating speed deviated by only 3%. That's pretty close to me.