Is speed (SOG) additive?

[rockDAWG]

Say....... Sailing without motor is 3 knots. Motoring alone at 1200 rpm is 3 knots. when using both together, do you get 6 knots assuming all others are the same.

[dillybar]

It would be possible to get close at some wind speeds and on some points of sail. But drag (air and water) increases with speed so you need to more than double the "push" to get double the speed there are other variables to consider as well including ultimate hull speed of the boat.

[DrB]

Once you reach hull speed, your at a limit of what you can do. Say you have sails up and doing 5 kts SOG. Say at full throttle on the motor, without sails up, you can get 7 kts SOG, and your hull speed is 7.5 kts. Then raising the sails is not going to get you to 12 kts, because your hull will limit you to 7.5 knots, assuming no current or surfing.

DrB

[rockDAWG]

Thanks Gentlemen, my scenario assumes the boat travels below the hull speed.

May be I did not post the question in a direct way. Let me ask the question directly.

Let's say....

1. I want to get back to home port as soon as possible with least amount of fuel.
2. Wind is blowing from ahead but is able to do the close hauled.

Should I full throttle or should I be motor sailing with a lower rpm? I hope I can maintain the same speed without full throttling.

[oceanscapt]

Sometimes (how's that for being committed?).

If I'm on a passage and I need to maintain a certain SOG to get to the anchorage before dark then I'm watching the display.

If I'm working on my sail trim then watching the SOG rise to a sustained level tells me I've got the sail trim right for that point of sail and conditions.

Other than that, I'm looking at the SOG and STW (speed through the water) to tell me about currents.

[Zanshin]

Resistance is complicated to compute and depends on many factors, but it is safe to say that resistance increases more than linearly with speed; the actual curve in still water and with an upright hull is more of a logarithmic curve (see p. 60 Principles of Yacht Design, Larrsson and Eliasson), i.e. a given boat at 4 knots has 250Newton resistance, at 6kn it is 750N and at 8kn it is 2800N and the resistance shoots up much higher when approaching hull speed.
Thus, adding the energy needed to motor at 3 knots to the energy needed to sail at 3 knots will most likely result in a boat speed of 4 knots rather than 6 knots.

[dillybar]

Of course, the most accurate way to take all the variables out of the equation would be to simply turn the motor on while sailing and note the speed increase. You can then decide if the increase in speed is worth the fuel consumption and noise etc.

[RichH]

Simple physics explanation is that there is a direct relationship between energy (horsepower, etc.) and speed (velocity).
The 'basic' energy equation is E = 1/2 m(v - 'squared') .... a 'quadratic' function. the constant 1/2 doesnt change and the mass m doesnt change ....

So putting in TWICE the energy (youve already defined 'sailing' (3 ikts.) as equivalent to running the motor alone @ 1200 rpm = 3kts) motor + sailing .....
now 2E (twice the energy) equates to the "square root of 2X the velocity";
sq. rt. of 2 = 1.4
So motor PLUS sails (under the same conditions) yields 3 X (sq. rt of 2) = 3 X 1.4 = 4.2 knots when sailing with the motor on AND the sails up ... all during the EXACT SAME conditions.

So, NO its not additive; its directly proportional to the *square root of the velocities*. The energy is additive, NOT the velocities.

[jcalvinmarks]

I'm kinda with dillybar on this one. The forumlas and numbers and calculations are great, but I think his suggestion gets right to the point with the least amount of arithmetic.

[ottos]

Originally Posted by rockDAWG

1. I want to get back to home port as soon as possible with least amount of fuel.

Two conflicting goals.

Shut off the motor - its a SAIL-boat !