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How thick would a mattress made of flower heads need to be to stop a child falling down a 200-ft deep hole from getting seriously hurt?

The child is 5 years old and of an average weight, the flowers are sunflowers of an average density, and they are arranged such that that their petals are facing up. This is on Earth. We are also assuming that the child doesn’t land in such a way that they die (for example landing on their head).

Note: This isn’t a mattress filled with flowers, it’s a mound of flowers.

Thanks!

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    $\begingroup$ As long as you're asking as a general thought and not only about Undertale, this question should be fine here. And it's kinda hard not to be general since Frisk, Undertale's main character, is an ultra-generic human child, and the fall's length and flowers are quite undescribed. We could use more details however : For your question, can we know the kid's age, and which kind of flowers do you want to use (hopefully not roses!)? $\endgroup$ Aug 25, 2022 at 23:29
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    $\begingroup$ Hello Alphys. Before I vote to close your question. (a) We do not answer questions about 3rd party or commercial worlds. (b) We do not know what the planetary gravity is in the game. (c) We don't knonw what flower petals are being used. (d) We don't know the length and width of the mattress. (e) We don't know the fabric properties of the material used to make the mattress. (f) We don't know anything about the child (those averages aren't as average as you think). (g) We don't know if the mattress is the size of the hole or not. And if we knew all that, (h) this would just be a math problem. $\endgroup$
    – JBH
    Aug 25, 2022 at 23:40
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    $\begingroup$ Also, "average weight and density" varies wildly depending on the child's age, and the flowers' species. $\endgroup$
    – jdunlop
    Aug 25, 2022 at 23:40
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    $\begingroup$ As an initial guess, 198 ft thick? (Assuming the thickness of the mattress is subtracted from the fall.) $\endgroup$
    – Jedediah
    Aug 26, 2022 at 0:31
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    $\begingroup$ Roses are red, violets are blue, if you know how to model their petals as liquids with certain kinematic viscosities then we need you! $\endgroup$
    – user86462
    Aug 26, 2022 at 3:24

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I shall assume that you are asking about a world you are building and using a 3rd party world as an example - otherwise this would be off topic.

Unfortunately, this is hard to answer because there is no meaningful "average" set of values for a group as broad as "flowers" that will help us work out how well they would behave as a mattress to safely land on. We also don't know what angle the child is landing at - hopefully not head first. Instead, lets assume that the flowers will compress/collapse in an ideal fashion to allow safe landing.

One of Newton's equations was taught to me as v^2 = u^2 - 2as, where:

  • v = final velocity
  • u = initial velocity
  • a = acceleration
  • s = distance travelled

This equation will govern the child's plummet 60 m downwards and the subsequent deceleration in the mattress-of-ideal-crashmat-flowers. In fact, if we ignore air resistance, due to the symmetry of the fall and subsequent deceleration we can solve for the thickness of the mattress by taking u, v and the constant "2" out of the equation and simply say that: a (falling) x s (fallen) = a (safe deceleration) x s (thickness of mattress)

People can, very briefly, withstand acceleration of 20G. Fighter pilots with G suits can remain conscious up to around 10 G. The space shuttle was deliberately limited to a peak acceleration of 3G because pretty much anyone was fine with that over the extended period of a launch. Let's pick a value in the middle and say that a child will be fine with 6G for a second or so of a flower-crushing landing. This means that:

Mattress thickness = (1 G x 60 m) / 6 G = 10 m

Wow, that's a pretty thick mattress (probably multiple horizontal nets of vines that successively broke away). It also means that the child needs an exit route or the 10 metres of vegetation that wasn't compressed on landing will be collapsing on top of them.

If you don't like that value then go for a G value you can live with (or, more to the point, hope the child can live with) and divide the distance fallen by it. Important safety tip - child should not try to jump on the "mattress" again until it has been regrown into a non-compressed configuration.

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    $\begingroup$ With such amount of flowers, I think the remaining questions are : would flowers really compress correctly and consistently over 10m ^^? And can we really stack them so they compress consistently on impact? $\endgroup$ Aug 26, 2022 at 1:49
  • $\begingroup$ landing on your back people can survive 30g , 300ft drops onto air bags (a little less than 10m thick) have happened and it has been demonstrated that foam works just as well if not slightly better than airbags, so assuming vegetation has the same cushioning as foam (a big assumption) this is completely believable. youtube.com/watch?v=3KwyftaLT-k $\endgroup$
    – John
    Aug 26, 2022 at 3:55
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    $\begingroup$ @Tortliena a literal pile of flowers 10 m high would compress so much under its own weight that the bottom layers would provide no cushioning at all. Frankly the only way it could work would be (flowering) vines growing horizontally in a net that would stretch and break away just as the child reached the next net that would stretch and break away and so on. Of course if a particular vine is too strong and doesn't break away then a new child is probably required, especially if the neck is caught. $\endgroup$ Aug 26, 2022 at 4:21
  • $\begingroup$ Thanks @KerrAvon2055 but I’m going to flag this question for deletion. It probably shouldn’t be on Worldbuilding. Sorry :( $\endgroup$
    – Alphys
    Aug 26, 2022 at 20:26
  • $\begingroup$ @Alphys Since your edit it's 3 votes out of 5 to be reopened :). Don't think a closure means the end! $\endgroup$ Aug 26, 2022 at 21:21

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