# Horsepower Multiple Boat Engines

The term horsepower was invented by the engineer James Watt. Watt lived from 1736 to 1819 and is most famous for his work on improving the performance of steam engines. We are also reminded of him every day when we talk about 60-watt light bulbs.

The story goes that Watt was working with ponies lifting coal at a coal mine, and he wanted a way to talk about the power available from one of these animals. He found that, on average, a mine pony could do 22,000 foot-pounds of work in a minute. He then increased that number by 50 percent and pegged the measurement of horsepower at 33,000 foot-pounds of work in one minute. It is that arbitrary unit of measure that has made its way down through the centuries and now appears on your car, your lawn mower, your chain saw and even in some cases your vacuum cleaner.

What horsepower means is this: In Watt's judgement, one horse can do 33,000 foot-pounds of work every minute. So, imagine a horse raising coal out of a coal mine as shown on the pdf. A horse exerting 1 horsepower can raise 330 pounds of coal 100 feet in a minute, or 33 pounds of coal 1,000 feet in one minute, or 1,000 pounds 33 feet in one minute. You can make up whatever combination of feet and pounds you like. As long as the product (multiplication) is 33,000 foot-pounds in one minute, you have a horsepower.

You can probably imagine that you would not want to load 33,000 pounds of coal in the bucket and ask the horse to move it 1 foot in a minute because the horse couldn't budge that big a load. You can probably also imagine that you would not want to put 1 pound of coal in the bucket and ask the horse to run 33,000 feet in one minute, since that translates into 375 miles per hour and horses can't run that fast.

• 1horsepower (hp) = 750 watts  = torque (rotational force) x RPM / 5,252
• 160,000,000hp: Saturn V Rocket
• 37,000,000hp: Space Shuttle
• 160,000hp: Boeing 747 airplane
• 6,600hp: train
• 170–190hp: typical American car
• 250–300hp: turbo or v6 options
• 275–300hp: pickup trucks
• 808 HP: 2018 Dodge Challenger SRT Demon R
• 5hp: scooter
• 25-65hp: motorcycle (100-150hp: sport bikes)
• 326hp: Kawasaki Ninja H2R
• .15 to 1 HP: humans generate 100watts just sitting; 200 watts working; 400 watts as an athlete

I shared that my 70hp 14 foot tender (dinghy) weighs 1,200 lbs. and has a top speed of 35mph; my 42 foot boat has 800 hp and I asked the children how fast do they think it goes. Although they did see a picture of the boat and could see it was much larger, many of them looked at a linear relationship: they reasoned that since the 800hp is about 11x the 70hp, that the 800hp boat must go about 11x 35 or about 385mph. Then I asked them to think about whether that is reasonable, like the horse going 375mph pulling one pound of coal. Then, they focused on the weight of the 800hp boat, which I then told them was 25,000lbs. or about 21x the 1,200lb. boat. Then, most of them reasoned that it must go somewhat less than 35mph. It actually has a top speed of around 30mph since it is more efficient than the 70hp boat.

I showed them dozens of pictures of boats with multiple outboard motors: twin, triple and even four engines. Then, showed them the ridiculous 5, 6, 7, 8, and yes, 9 outboard engine boats. They were tasked to add up the total horsepower using several algorithms:

• for the K/1 Mathletes, I gave them an easy page with numbers like 2 x 100,  2 x 200, 2 x 300, 2 x150, and so on (I also gave them the challenge pages but I do not expect them to get those; just getting them familiar with large numbers can be fun)
• multiplication is just repeated addition (so for twin 250hp, they could add the numbers vertically with carries to generate 500hp)
• the most intuitive method is distributive property where you distribute the number of engines to each place value of the horsepower (3 x 350 would be 3 x 300 =900 and then 3 x 50 = 150 and then just add 900 + 150 = 1,050).
• I also gave them a page with triple and quadruple engines with no numbers: they can make up any number horsepower they want and multiply it by 3 and 4. My algorithm for multiplying by three is called double-add (first double the number and then add that double to the original number); for four, just double twice; for eight, double three times and so on.

Fun Work:

This work is intended to be challenging for most and the children should feel free to work with parents or a caregiver. Just show effort and they will earn Mathlete Dollars.

Answer keys are provided in the pdf.

Also, they can do as much research as they like such as finding the horsepower of their own family cars, cars that they know like the Bugatti Veyron https://www.caranddriver.com/bugatti/veyron. Just have fun.

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