The Question
In a recent post seen on a Facebook, the question was posed (link here):
“Why does everyone talk about horsepower and rarely about torque, but everyone at the same time screams big cubic inches as this is what moves the boat.”
The simple answer is because horsepower is all that matters. Of course, a simple statement won’t convince the torque advocates, and it shouldn’t because they do have a point. They are just not very proficient at justifying their point from an engineering perspective. That’s where Allmond Marine can offer some guidance.
What is Power? What is Torque?
Memes are sometimes an efficient way of conveying thoughts. Not every meme is accurate, however.
What the captain above is contemplating is better called “speed” and “inertia”, but I digress…
Power is simply the rate at which a machine can do work. Here’s the classic equation you’re familiar with, but expanded to show where the “5252” constant comes from.
But what does this have to do with boats?
Drag
Of course, boats are drag-limited vehicles. As such, their maximum speed is where there is a balance of thrust and drag. The power to overcome a given value of drag is proportional to velocity cubed.
Find below a plot of required propshaft horsepower versus velocity. This is specific to a 12,000lb boat without steps. As you can see – going 100mph in such a boat would take an extreme amount of power – 8400Hp per this model. This is precisely why stepped hulls exist!
Finding the Balance
Since I’m an engine valvetrain specialist, and not a prop specialist, I have to turn to an expert in that field to tie this all together. In the figure below, I’ve scanned a figure from Propeller Handbook by David Gerr (©1989). On this plot, he explains clearly the relationship between engine horsepower and power demand for a boat. As he describes, most people choose a prop by picking the one that produces the maximum RPM at the peak power speed. It’s the way it’s been done for years.
In fact, it’s been done that way for so long, that the propeller industry has tuned in on combinations of diameter, pitch, and so on that work very well for the common combinations out there. For offshore powerboats, that typically means Chevy big-block based power, with or without a supercharger. The market is full of props that complement this engine’s ample mid-range power characteristics.
But then there’s the oddball powerplants: Viper V-10’s, QC4V 860’s, and so forth. They make the power, so why don’t they run as good? My take is that the props for those combinations largely don’t exist, so the prop selections are largely suboptimal. Below I’ve plotted a higher-revving engine with equivalent power to the black line drawn by Dave Gerr. If you imagine that black line as a supercharged big-block, an NA QC4V 860 (blue line) will rev higher, but make less power in the midrange. While the optimal prop selection would be the solid gold line, what’s available is the dashed gold line, which gives significantly less performance.
Acceleration, per the Physics
Some of you may be familiar with Isaac Newton’s second law:
It is from Newton’s second law that we get the basic way that propeller’s produce thrust: they take a column of water and accelerate it. That force is what we call thrust.
And you may also be aware that force times velocity is equal to power:
Using the two equations above, we can do something interesting: We can prove that acceleration is proportional to power (not torque!)
If:
Then:
Substituting in Newton’s second law:
Then, if we assume mass is constant, and velocity is non-zero, we can reduce this to:
So, if you want to accelerate harder, you need to put more power to the water. Hands down. You can do that through displacement or boost.
Of course, it would be equally valid to say that torque over time is proportional to acceleration, but it’s not nearly as elegant.
Looking back at Dave’s chart, acceleration can be found there too:
I’ve added blue lines to highlight that acceleration is proportional to the amount of horsepower (P in the equation above) you have above the propeller power curve. If you can apply more power (or ft-lbs/sec for you torque junkies) than the prop power curve, you will accelerate. If your engine has more midrange power (or torque per second), you will accelerate harder in the midrange (yay blowers!). You can also see that You can extend those lines down to Prop Power Curve B, and get even more acceleration, until you overspeed the engine. In either case, when the engine power and prop power lines touch, you’ve hit top speed (or grenaded your engine before you got there).
In summary we’ve learned three main things:
- It is power that is required to move a boat through the water, aka torque per second.
- Power is proportional to acceleration
- Props are always critical, and may need to be developed for non-standard engine packages
Be sure to check back for more tech from Allmond Marine!
