A Date Idea Analyzed

Posted byRandall 487 Comments on A Date Idea Analyzed

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.

487 replies on “A Date Idea Analyzed”

  1. Just use a helicopter. You can sit in it, watch the sunset and then rise several times to watch it again. The price of renting one would be high, but cherrypickers aren’t cheap to begin with.

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  2. or you can rent a balloon accelerating in synch with the time and watch the sunset in stasis in the horizon

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  6. I’ve tried this in a plane before, so I know it works, but I would love it if someone would do the math to figure out how moving laterally at about 100 knots affects the time and height required. The time it didn’t work I think was because we were heading east. I hit a climb rate of greater than 1300 feet per minute for about 15 seconds, then about 500 fpm after that and wasn’t able to get the sun to come up again.

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  7. Well how about simply including an elevator in the equation. Rater than a cherry picker, have a date next to a skyscraper. Then after the sunset, go up to the observation deck and do it all again. This would probably work best in a city like Dubai.

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  8. So, I live in an hour from Boise, Idaho right now. Anyone have any ideas for cities with the nearest skyscraper near the coast? I have resolved to try that idea.

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  9. A big flaw in this plan is the fact that for OH & S reasons, if you’re going over 2m high you need to be wearing a harness. Now those things are just not sexy, even if you’re into bondage.

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  10. funfact!
    well, due to the refraction of the earth’s atmosphere the sun actually sets below the tangent. (well, from the sun to you) and you see it set roughly 5 minutes after is already has.
    doesn’t really affect the problem too much though.

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  11. Well, in this case the experiment is much easier than the math. One simply needs to observe the sunlight on a tall structure, like a building, a week or so before. There are many beach houses that would serve this purpose (and taking her to a beach house would make a much nicer date, anyway.)

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  13. OK so the problem for me is that when we think of a sunset we don’t think of an instant in time. THis is especially true at the ocean. What happens is that the sun appears to sink into the sea like its a submarine. This takes time to occur. The Cherry picker could prolong the sunset but it can’t create two distinct sunsets. To do that you need to do something like what matt said and watch the sun set over a rise and then climb to the top of it. Also if you are looking for a really prolonged sunrise I suspect that you could go to the Artic circle at the right time of year. I know that there are a few days in the year where the sun doesn’t set at all. But I suspect there is a location and path that you could take that would result in a very prolonged sunset.

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  14. Aren’t you forgetting latitude? I’ve seen the sun set in the tropics, and I’ve seen it set near the arctic circle. The first takes minutes, and the second takes hours.

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  15. I have been told by someone who saw it more than once that, if you took the Concorde from London to New York at the right time of year, you could see the sun set while you were on the ground, then rise as the plane rose to cruising altitude, and then set again. Not quite the same as the cherry picker on the beach, though.

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  16. There’s a similar idea in Julian Barnes’ novel “Staring at the Sun,” involving airplanes and rapidly climbing or descending to see a sunset or sunrise twice.

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  17. Seems like you could do this in a tall enough building given a skyline that is conducive to seeing a sunset. Perhaps a Miami beachfront condos with one of those external glass enclosed elevators?? (other examples exist, I’m sure)

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  18. Okay… Suggesting to spend incredible amounts of dollars to rent a cherry picker and pick her up. Definitely not early dating material, definitely for someone very deserving who have demonstrated she is worth something worth that much effort.

    Sosuave.com

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  19. I, frankly , would Marry any woman who turned up at my door and did that.

    And if I was a girl, vice versa.

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  21. dude, submit it to mythbusters xD idk if that was already suggested…. i did’nt really look, btw, love the comic

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  22. 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.

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  23. 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!”

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  26. 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.

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  27. 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…

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  28. “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)

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  29. 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.

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  31. 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*

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  36. 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)

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  38. 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.

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  40. [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?

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  42. 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 :-P.

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  43. 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.

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  44. 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.

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  45. 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).

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  46. 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 🙂

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  48. 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.

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  50. I didn’t read all of the comments, but I did note that refraction was also neglected. Just saying.

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