I don’t do conventions very often, but I recently went to ConBust out in Northampton, MA, while visiting some friends. While I was there, I had a guy propose something fascinating to me. I can’t remember the guy’s name, so if he or one of his friends sees this, post your info in the comments. (Edit: it was a dude by name of Thom Howe.)
The guy Thom had an idea for a date. He wanted to rent a cherry picker, drive it to her door, and pick her up in it.
Then, he’d drive to the beach, and get there at just the right time to watch the sun set.
Once the sun had set, he’d activate the cherry picker, they’d be lifted up above the beach …
… and they’d watch the sun set again.
Clearly, this is an excellent idea, and any girl would be lucky to see this guy Thom at her door. But is it plausible? How fast and how high does the cherry picker have to go?
I tried to work out the answer for him there at the table, but there was a line of people and there wasn’t time. But when I got home, I remembered it again, and I’ve worked out the solution.
Here’s the situation:
By the time the earth has rotated through angle theta, the cherry picker will have to have climbed to height h.
After t seconds, theta in radians is:
The height of the lift above the center of the earth is:
So the height above the surface (sea level) is:
Substituting everything so far we get this expression for the height the lift needs to reach t seconds after sunset to stay even with the sun.
Now, an actual cherry picker has a maximum lift rate (I Googled some random cherry picker specs, and 0.3 m/s is a normal enough top lift rate.) We’ll call that rate v, so the actual height of the lift will be this:
Substituting that in and solving for v, we get this:
(That’s arcsecant, not arcsecond). This equation tells us how fast the lift has to go to get from the ground to height h in time for the sunset1.
But we can also get the answer by just trying a few different heights. We plug it in to Google Calculator2:
2*pi*6 meters/(day*arcsec(6 meters/(radius of earth)+1))
and find that h=6 meters gives about the right speed. So, given a standard cherry picker, he’ll get his second sunset when they’re about six meters up, 20 seconds later.
You might notice that I’m ignoring the fact that he’s not starting at sea level — he’s a couple meters above it. This is actually pretty significant, since the sunset line accelerates upward, and it brings down his second-sunset height quite a bit. If he got a faster lift, or used an elevator, the correction would become less necessary. Extra credit3 for anyone who wants to derive the expression for the height of the second sunset given the lift speed and height of first sunset. For now, I recommend he dig a hole in the sand and park the lift in it, so their eyes are about at sea level4.
1 Ideally, we’d solve for h, but it’s inside the arcsec and that looks like it’s probably hard. Do one of you wizards with Maple or Mathematica wanna find the result?
2 If you work in one of the physical sciences and don’t use Google Calculator for all your evaluatin’, you’re missing out. I wish there were a command-line version so I could more easily look/scroll through my history. I know Google Calculator is largely a frontend to the unix tool units, but it’s better than units and available everywhere.
3 Redeemable for regular credit, which is not redeemable for anything.
4 I suggest a day when there aren’t many waves.
I, frankly , would Marry any woman who turned up at my door and did that.
And if I was a girl, vice versa.
Anyone know where I can hire a cherry picker?
dude, submit it to mythbusters xD idk if that was already suggested…. i did’nt really look, btw, love the comic
This is what I would do: pick up normally, go to sunset picnic at beach next to cherry picker, watch sunset, climb into cherry picker, ascend, watch again, win.
As a counter suggestion, I believe someone would get a lot of pull out breaking up this way too -
“It’s over, just like that sunset, baby!”
“Nooo, can’t we just be friends?”
(Launches spurned lover high above the waves with a catapult, where he or she sees the second sunset)
“Don’t make me repeat myself!”
This makes me happy that I am marrying a scientist next weekend. They are so cute.
Copied to a girl I’ve been dating and I’ve gone to the beach with…
ftw!
Why not find a tall building with an express elevator? The top floor is probably not a good idea, because of the accelerating height required, but another floor might be able to just about do it.
Yes, a glass/steel stuctured building, or at least with a very large window on the ground floor facing West, and a clear view of the horizon. It might be possible to do it going from one floor to a higher one, but you’re at a disadvantage.
Wait a minute… GLASS ELEVATOR! Now that’s awesome.
If a girl showed up at my door in a cherry picker and started talking math to me we’d never make it all the way to the beach. Math is sexy…
“It’s over, just like that sunset, baby! No, can’t we just be friends? Launches spurned lover high above the waves with a catapult, where he or she sees the second sunset)
My wife and I actually did this quite by accident on our honeymoon, passing through Montecatini. Saw one sunset from the foot of the mountain, took the funicular railway up to the top and had another one.
Very good, congratulations article
Perhaps this would be the perfect way to propose to someone, as you obviously need to care about someone greatly to spend the sort of money needed to rent a cherry picker. I still think its awfully romantic. Its so sweet. *melty face*
I am grateful to you for this great content.
This is what I would do: pick up normally, go to sunset picnic at beach next to cherry picker, watch sunset, climb into cherry picker, ascend, watch again, win.
I, frankly , would Marry any woman who turned up at my door and did that.
And if I was a girl, vice versa.
If a girl showed up at my door in a cherry picker and started talking math to me we’d never make it all the way to the beach. Math is sexy…
http://wolframalpha.com is also really great for units, and all sorts of other sweet calculations (typing in “iss” will tell you where the international space station is at any given moment, or you can find out the weather on the day of your birth! or add colors, even)
Umm.. what about diffraction?
I’ve seen a number of 2nd…and 3rd and 4th sunsets from small airplanes, practicing stalls at sunset. Definitely interesting, but most girls don’t like it.
This will definitely impress my girlfriend. Thanks for the tip.
[2] I create an alias wrapper to “awk” to do all my command-line math (in tcsh form below–translate to bash as needed):
> alias calc ‘awk “BEGIN{print \!#}”‘
> calc 2*3.14159*6/( 86400*atan2 ( sqrt ( 6* ( 6+2*6378 ) ) ,6378 ) )
0.0100633
Okay, that’s not 0.3 m/s. Who screwed up?
Oh, yes, kilometers versus meters… I’m always dropping three orders of magnitude…
> calc (2*3.14159*6/(3600*24*atan2(sqrt(6*(6+2*6378000)),6378000)))
0.318104
Here’s the solution for factoring in the fact the original height above sea level.
v = -2*Pi*(-h[2]+h[1])/(arccos((h[1]+r[e])/(h[2]+r[e]))*d)
I will post my full solution at a later date as I’m a bit pressed for time at the moment. Let me just say it involves constructing two triangles, similar to the one above. Full details (and hopefully diagrams) to follow.
PS This is a perfect example of nerd-sniping! I dropped everything when I saw this and am now running a little late
.
Cheap version: lie down on the sand, just out of reach of the waves (or just within reach, depending on weather). The nstand up as soon as sunset one has happened. Sunset two follows a few seconds later.
In your calculations, you have overlooked the refraction of light in our atmosphere. Your model is a reasonable approximation – but I believe that refraction slows the perceived setting of the sun! That is, the lower the sun gets, the greater the refraction and the the longer it remains visible.
So a shorter, slower, more slovenly lift might actually do the trick.
Regrettably, I have not the math skills to quantify this affect.
Rather than using a cherry picker to enjoy a second sunset I believe if you are on a West coast with an ocean you can use the reflection of the sun to get the illusion of a secondary sunset (or one really long slow sunset).
well don’t you think it much easier just to watch the sunset from a building next to the sea, and the go to the much faster elevator? though it’s much less romantic
Patanol…
I don’t do conventions very often but I recently went to ConBust out in Northampton MA while v [...]…
Is your line to the top of the sun or the bottom of the sun or the center of the sun, which is 1920 arcseconds (.533 degrees)? It seems your calculations should be based on when the top of the sun is under the horizon, and getting the lift high enough to see the bottom of the sun. This adds non-trivial timing and height requirments.
I didn’t read all of the comments, but I did note that refraction was also neglected. Just saying.
another interesting stunt would be bungeeshooting right after the sun sets, that way you might get serial sunsets.
Much as I hate to burn holes In a beautiful idea, I can see one thing wrong in this logic.
I would consider a sunset not to be a fixed moment in time, but to be the whole duration In which the sun sinks over the horizon. The shortest period of time this could be defined as is from when the lowest part of the sun appears to just touch the horizon (so the horizon appears like a tangent), to when the sun can no longer be seen. A definition of a sunset which would give a longer time would be the period of time when the suns light is refracted so It appears red.
The calculations shown here give the rate of climb that would have to be maintained for the sun to appear in the same position relative to the horizon. For the same sunset to be experienced twice you would have to wait until the sun has sunk, and then elevate yourself at a rate faster than the one given here, until the sun appears right above the horizon again.
This would take a different period of time depending on how long the sun took to set, which is different at all times of the year, (unless you happen to live at the equator).
This is not to say that the answer given by this calculation is useless. When Space Elevators are developed, this is the rate at which they will have to climb for people in them to enjoy a (semi) perpetual sunset. Now I for one think that that is a great date idea.
Yours In Maths
Hungry_Joe
While on vacation a few weeks ago, I had a thought that led me down a similar line of reasoning:
How “curved” is lake tahoe? I.e., if you set a perfectly flat plane down at lake level on one shore, how far below the plane would the lake be at the opposite shore, 22 miles away, due to the curvature of the earth?
Using similar math, you wind up with somewhat surprising answer: 300 feet. I had to double check that a few times.
Long time reader of XKCD, first time poster.
I get the math, and I have done this very thing; but with a Cessna airplane.
flew straight and level at slow cruse. A second after the sunset from view, pushed the throttle in and pulled up. Second sunrise and sunset of the day. Very cool and I got the girl!!
