# Convert horsepower to duck power

DingusDev42

## Main Question or Discussion Point

Okay, so maybe this is the wrong forum. I'm here as a last resort, I've been on 4Chan and ask websites for three hours just looking for ideas, or God willing, some real data.

I've been tasked by a friend to convert horse power into duck power. It sounded easy at first but I'm stuck. I've barely gathered any data and I can't think of how to move on.

1 Horsepower = ~750 Watts or 550 foot-pounds per second

The only lead have is that a duck in DnD has a strength attribute of 3, but I don't play DnD so I don't know if that means anything in real world terms.

It's okay if some logical reaches are made, considering the silly nature of this project. If you have an idea concerning where I should look, like a different forum or website, I'm all ears.

Related General Discussion News on Phys.org
Okay, so maybe this is the wrong forum. I'm here as a last resort, I've been on 4Chan and ask websites for three hours just looking for ideas, or God willing, some real data.

I've been tasked by a friend to convert horse power into duck power. It sounded easy at first but I'm stuck. I've barely gathered any data and I can't think of how to move on.

1 Horsepower = ~750 Watts or 550 foot-pounds per second

The only lead have is that a duck in DnD has a strength attribute of 3, but I don't play DnD so I don't know if that means anything in real world terms.

It's okay if some logical reaches are made, considering the silly nature of this project. If you have an idea concerning where I should look, like a different forum or website, I'm all ears.
Minimum cost of transport for a swimming duck is 5.77 kcal/kg per km. (https://books.google.com/books?id=U64JafOXDWkC&pg=PA133&lpg=PA133&dq=metabolic+rate+of+ducks&source=bl&ots=BxgPCY3HSm&sig=d7ZqsNDQOO1jYkx4WW-Jz5AXq7Q&hl=en&sa=X&ved=0ahUKEwjizJfLy5PQAhUFQyYKHXe6Cd44ChDoAQgaMAA#v=onepage&q=metabolic rate of ducks&f=false) if the average weight of a duck is 2 kg, thats about 2.8 kcal per kilometer. if a duck can swim at .7 m/s, converting that to km/s gives .0007km/s. Now mulitply this to the cost of transport and you get 5.77*.0007/2 $\approx$ .00202 kcal/s.
I shall leave the dimensional analysis for finding the conversion factor up to you.

Simon Bridge
Homework Helper
Power would be the ability to do work continuously - if you want DnD appropriate stuff, then compare the stats, probably for dragging or carrying a load.
A light load for a light horse is up to 150 pounds; a medium load, 151–300 pounds; and a heavy load, 301–450 pounds. A light horse can drag 2,250 pounds.
http://www.dandwiki.com/wiki/SRD:Light_Horse
... no stats for a duck (avian) and animals do not have the strength, etc type stats that PC's do.
You'd have to look for closest likely creature: http://www.giantitp.com/forums/showthread.php?275156-Stats-for-birds

Phyiscally, you will want to figure out how "horsepower" is defined in terms of work done by horses, and then find data for what ducks can do.
Consider: Are the ducks walking, swimming, or flying?

Ultimately the conversion will depend on what you want to do with it - why is it relevant?

@Jamison Lahman : wow - just.... wow.
8.45W or very roughly 1% of 1hp for swimming.

Randy Beikmann
Gold Member
I don't know any references researching duck power, but Monty Python provides some clues about swallows. Apparently, two European swallows should be able to carry a coconut together, using a string held under the dorsal guiding feathers.

No research cited, as these observations were made in medieval times. But if you assume a diameter and drag coefficient for the coconut, and a cruising speed, you can at least estimate the aerodynamic power. I'd have to think about the power required to carry the weight.

OmCheeto
Gold Member
Solving the point slope equation for humans and horses, where:
The average human weighs 137 lbs, and can sustain 0.1 hp, and the average horse weighs 1100 lbs, and obviously can sustain 1.0 hp​

It is quite clear what the average duck, weighing 7.5 lbs, is capable of.

The answer is a tad less than Jamison Lahman's solution, as his duck was swimming, and mine, was not.

[references available upon request]

Simon Bridge
Homework Helper
Consider references requested ... all the time, every time.
In a scientific forum, citations are always requested, by default, for any claim.

OmCheeto
Gold Member
Consider references requested ... all the time, every time.
In a scientific forum, citations are always requested, by default, for any claim.
References:

Weight of an average horse: 1100 lb
https://www.reference.com/pets-animals/much-average-horse-weigh-289a0e909645d02d

weight of an average duck: 7.5 lb = 3.40 kg

weight of an average human: 62 kg = 136.69 lb

average hp of 1 human = 0.1 hp
https://en.wikipedia.org/wiki/Horsepower

Also: Kleiber's Law
https://en.wikipedia.org/wiki/Kleiber's_law
Kleiber's law, named after Max Kleiber's biological work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the ¾ power of the animal's mass. Symbolically: if q0 is the animal's metabolic rate, and M the animal's mass, then Kleiber's law states that q0 ~ M¾. Thus a cat, having a mass 100 times that of a mouse, will have a metabolism roughly 32 times greater than that of a mouse.

weight ratio horse to duck = 146 2/3
(146 2/3)^(3/4)=42.1
1/42.1 = 0.0238 hp [duck]

This is roughly 3 times my calculation.

DaveC426913
Gold Member
weight ratio horse to duck = 146 2/3
(146 2/3)^(3/4)=42.1
1/42.1 = 0.0238 hp [duck]
Resulting in the answer of 42, to within 1 part in 3000.

jim mcnamara
Mentor
@OmCheeto if nothing else you get high marks for persistence!

jim mcnamara
Mentor
@DaveC426913 Yup. Douglas Adams is prize winning physicist. Or is that psychic? 42 is the answer to everything as I see you realize fully.

DingusDev42
Wow, you guys are great. You may be interested to know that I reached out to /tg/ on 4Chan. I figured they'd have some input since I tried using DnD stats. They all came up with some really interesting math and the answers ranged between 25 and 60 duck power per horsepower, with some outliers.

@DaveC426913 Yup. Douglas Adams is prize winning physicist. Or is that psychic? 42 is the answer to everything as I see you realize fully.
42 isn't the answer to everything like everyone thinks, it's the answer to the ultimate question of life, the universe and everything. But no one knows what the ultimate question of life, the universe and everything is. Which is good too, because no one world can know both the question and the answer, because knowing both causes the universe to cease to exist.

OmCheeto
Gold Member
@OmCheeto if nothing else you get high marks for persistence!
I initially considered modeling a spherical duck versus a spherical horse, but things got a bit complicated, so I just googled stuff, and did a few calculations.
I was also curious how to verify the output of ducks, so I imagined 42 ducks in a tug of war contest with a horse. Googling was not my friend.
But I did find a horse which won a tug of war contest against 50 men[ref], so this leads me to believe that a tug of war contest may not be the best test of power output, as 10 men should have been the horses equal.

the answers ranged between 25 and 60 duck power per horsepower
Excellent! I was just tabulating the results so far. I'll add those two numbers, and one more for good luck:

Code:
hp/dp  dp/hp
0.0070  143  Interpolation by horse, human, duck, point slope method
0.0073  137  Fine structure constant[why not]
0.0133   75  Jamison Lahman's reference. [see note 1]
0.0167   60  4Chan upper range
0.0238   42  Kleiber's Law
0.0400   25  4Chan lower range
note 1: Interestingly, his reference listed Kleiber's name and is dated 1961. The wiki entry dates his work to the 30's. Which meant he was doing duck power experiments for at least 30 years. Now that's persistence.

Max Kleiber [wikipedia]

FactChecker
Gold Member
2018 Award
I don't know any references researching duck power, but Monty Python provides some clues about swallows. Apparently, two European swallows should be able to carry a coconut together, using a string held under the dorsal guiding feathers.

No research cited, as these observations were made in medieval times. But if you assume a diameter and drag coefficient for the coconut, and a cruising speed, you can at least estimate the aerodynamic power. I'd have to think about the power required to carry the weight.
What do you mean? An African or European swallow?

Simon Bridge
Homework Helper
...
42 isn't the answer to everything like everyone thinks, it's the answer to the ultimate question of life, the universe and everything. But no one knows what the ultimate question of life, the universe and everything is. Which is good too, because no one world can know both the question and the answer, because knowing both causes the universe to cease to exist.
... the theory is that it will be instantly be replaced by something even more inexplicable. There is another theory that says this has already happened. Perhaps I'll have another glass of whiskey ... yes, that seems more likely.

FactChecker said:
What do you mean? An African or European swallow?
Doesn't seem to matter:

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All said and done, then, a duck should be able to crank out 17 watts if you could get it to turn a wheel somehow, maybe a duck adapted bicycle pedal affair hooked to an alternator or generator. Train it with tidbits till it gets the hang of it and do a dynamo check on the beast:)

DaveC426913
Gold Member
weight ratio horse to duck = 146 2/3
(146 2/3)^(3/4)=42.1
1/42.1 = 0.0238 hp [duck]
Resulting in the answer of 42, to within 1 part in 3000.
Oh. I didn't see that you inverted 42.1 to get the decimal.

My answer actually took your .0238 and inverted it, but I got 42.015.

OmCheeto
Gold Member
Oh. I didn't see that you inverted 42.1 to get the decimal.

My answer actually took your .0238 and inverted it, but I got 42.015.
Given that I know of no fractional ducks, I believe that your inference that 42 is close enough to the answer, makes me trust that Mr. Adams was correct.

When comparing ducks to horses, 42 is always the common denominator.

This all seems pretty much a waste of time, particularly when we observe that 1 hp has little or no bearing on the power output from any particular horse at any particular instant.

This all seems pretty much a waste of time, particularly when we observe that 1 hp has little or no bearing on the power output from any particular horse at any particular instant.
Its not a waste of time for those entertained by it. Waste, is a relative term. While i see no use for my old aluminum cans and foil, i would throw them in the trash, to someone who uses aluminum for something such as making aluminum cast models, they would find my actions wasteful. Do refer to the old adage, one man's trash, is another's treasure.

DaveC426913
Gold Member
...no one knows what the ultimate question of life, the universe and everything is....
Yes they do. Marvin read it off, in the last book.

What do you get when you multiply six by nine.

Mech_Engineer
Gold Member

Since Ducks probably expend the most energy during flight, I would approach the "Duck Power" problem by estimating how much energy they expend during flight. We will for the moment, assume 1 hp = 745 W.
1. It is stated by Ducks.org that an average size hen mallard duck will burn approximately 1.8 million calories during a 1,500 mile flight from Saskatchewan to Louisiana
2. It is also stated by Ducks.org that most waterfowl species average about 50 mph during flight
3. Based on this speed, a 1,500 mile flight takes a duck about 30 hours flight time
4. 1.8 million calories expended in 30 hours calculates to 1 Duck Power = 69.8 W (0.094 hp)

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Since Ducks probably expend the most energy during flight, I would approach the "Duck Power" problem by estimating how much energy they expend during flight.
This seems like a hasty assumption. I would imagine ducks have optimized their flight capabilities as well as the fact they are likely going to try to expend the fewest calories during a 1,500mi flight. An analogy would be how humans expend more calories in water than on land. I am not a physiologist, but something to think about nonetheless.