Mythbuster's Exploding Water Heater
17/04/08 21:18 Filed in: Physics
In case you never saw it, here is the part of the
episode where the Mythbusters explode a water heater.
I started to analyze this previously, but it wasn't complete. Now I will finish what I started.
If you are curious, here are the "answers":
Time of flight = 11.8 seconds.
Max height = 167 meters = 548 feet
Speed on impact (ground) = 34 m/s = 76 mph (compared to 234 mph initially).
I started to analyze this previously, but it wasn't complete. Now I will finish what I started.
If you are curious, here are the "answers":
Time of flight = 11.8 seconds.
Max height = 167 meters = 548 feet
Speed on impact (ground) = 34 m/s = 76 mph (compared to 234 mph initially).
First, from re-watching the video, I can see (and
hear) that they used a 30 gallon water tank. By the
looks of it, this tank is about 3 feet tall with a
diameter between 1.5 and 2 feet. Can I find the
specifications of this water heater (or one similar)?
No luck at Lowes, they had some 30 gallon tanks, but they looked too skinny.
Here is a shot of the one the Mythbusters used:
How about Home Depot? - no. I
found one that is an electric 30 gallon water
heater. It is 36.5 inches tall and a 20.5 inch
diameter. This looks good. I need the mass
though. Well, I found a 40 gallon water heater
that had a weight (with box and everything) of
115 lbs. I am going to randomly pick a weight of
75 lbs. (I am assuming that the water all
explodes out at the beginning so that it is a
projectile, not a rocket).
Here is the goal - to estimate how high this heater went? In the episode, they exploded a water heater without a house around it. This heater was in the air for about 11 seconds. I assume they used the same model in the water heater that went in the building. I would love to use the video from the first, building-less explosion but they did not have the camera zoomed out far enough. They probably did not think it would go too high. I need the dimensions to get a good estimate for the air resistance.
The questionable value is the coefficient of air resistance. The water heater should have a value between 0.4 (rough sphere) to 2.1 (smooth brick). I will try with each one and see what kind of results I get. I am using the methods described here (numerical calculations).
Actually, I need to go back and look at my first calculations. If you don't recall, I scaled the video by assuming the manlift was 24 feet. I would like to revise my scale. I found a manlift that comes with a 40 ft boom, that is what I will use. In the video, I measured the lift to be 41.8 mb (mythbuster units). This would make 1 mb = 0.29 meters. So, the initial velocity will be 365 mb/sec = 106 m/s.
So, here are the parameters I am starting with:
mass = 25 kg
radius = 0.26 m
coefficient of air resistance = 1.4
initial velocity = 125 m/s
This gives data similar to the data from the video (during the first second). Here is the data from the video:
And here is data from the numerical calculations:
One thing to note: First, this
is not constant acceleration motion (although I
fit a quadratic equation to the data).
Nonetheless, a quadratic fit gives similar
accelerations in each case (it is near to
constant acceleration for the first second
because the speed does not dramatically change).
Now to run the simulation for the full time and see how high it goes and how long it was in the air.
The answer:
The calculations have:
Time of flight = 11.8 seconds.
Max height = 167 meters = 548 feet
Speed on impact (ground) = 34 m/s = 76 mph (compared to 234 mph initially).
Assuming the initial speed were correct and there was NOT any air resistance, the height would be:
time of flight = 25 seconds
max height = 797 meters = 2,600 feet
This analysis seems reasonable. I do not have a speed for the heater on the way down because the camera was moving, but it clearly was moving slower than when it took off.
No luck at Lowes, they had some 30 gallon tanks, but they looked too skinny.
Here is a shot of the one the Mythbusters used:
How about Home Depot? - no. I
found one that is an electric 30 gallon water
heater. It is 36.5 inches tall and a 20.5 inch
diameter. This looks good. I need the mass
though. Well, I found a 40 gallon water heater
that had a weight (with box and everything) of
115 lbs. I am going to randomly pick a weight of
75 lbs. (I am assuming that the water all
explodes out at the beginning so that it is a
projectile, not a rocket).
Here is the goal - to estimate how high this heater went? In the episode, they exploded a water heater without a house around it. This heater was in the air for about 11 seconds. I assume they used the same model in the water heater that went in the building. I would love to use the video from the first, building-less explosion but they did not have the camera zoomed out far enough. They probably did not think it would go too high. I need the dimensions to get a good estimate for the air resistance.
The questionable value is the coefficient of air resistance. The water heater should have a value between 0.4 (rough sphere) to 2.1 (smooth brick). I will try with each one and see what kind of results I get. I am using the methods described here (numerical calculations).
Actually, I need to go back and look at my first calculations. If you don't recall, I scaled the video by assuming the manlift was 24 feet. I would like to revise my scale. I found a manlift that comes with a 40 ft boom, that is what I will use. In the video, I measured the lift to be 41.8 mb (mythbuster units). This would make 1 mb = 0.29 meters. So, the initial velocity will be 365 mb/sec = 106 m/s.
So, here are the parameters I am starting with:
mass = 25 kg
radius = 0.26 m
coefficient of air resistance = 1.4
initial velocity = 125 m/s
This gives data similar to the data from the video (during the first second). Here is the data from the video:
And here is data from the numerical calculations:
One thing to note: First, this
is not constant acceleration motion (although I
fit a quadratic equation to the data).
Nonetheless, a quadratic fit gives similar
accelerations in each case (it is near to
constant acceleration for the first second
because the speed does not dramatically change).
Now to run the simulation for the full time and see how high it goes and how long it was in the air.
The answer:
The calculations have:
Time of flight = 11.8 seconds.
Max height = 167 meters = 548 feet
Speed on impact (ground) = 34 m/s = 76 mph (compared to 234 mph initially).
Assuming the initial speed were correct and there was NOT any air resistance, the height would be:
time of flight = 25 seconds
max height = 797 meters = 2,600 feet
This analysis seems reasonable. I do not have a speed for the heater on the way down because the camera was moving, but it clearly was moving slower than when it took off.
