[Closed] Maths people - please help me calculate volume!

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https://en.wikipedia.org/wiki/Spherical_cap

so V = 1/6 x Pi x 0.8m x (3 x (2.69/2)^2 + 0.8^2)

2.53m2?

Ace! Cheers.

Having just looked at this, I would use the fact that the depth of the spherical cap is 83cm. Then use pythagoras to give you the radius of the sphere which comes out as approx 200cm. Then use volume of revolution using the equation x^2 +y^2=200^2 integrating using the limits of 113 and 200. Never knew there was a formula for this.
Maybe wrong though.

Excavated soil is roughly 1.5 times the hole so 2.53m2 would require just under 4m2 space.

Excavated soil into a skip? Have you not seen the Great Escape?

Excavated soil is roughly 1.5 times the hole so 2.53m2 would require just under 4m2 space

I've no idea about the answer, but one does not measure volume in square meters. Is that a typo or a miscalculation?

my typo. m3

You could calculate the volume of an Oblate Spheroid and divide the result by 2.

Dig another hole and put the soil in that.

For digging and building and skip filling I'd just calculate it as a disc to the depth of the sphere bit and that would allow for the increase in volume due to digging out.

First, find out what size skips are available. You need a larger skip than the volume of dirt. The volume of uncompacted dirt will be larger than the volume of the hole, but that will depend on the type of soil, moisture content, and how much you compact it in the skip. That means you can only get a very rough estimate of the minimum size skip you need, so there's no point in using integral calculus to calculate it to 3 decimal places. Ignore that you're excavating a sphere, just assume you're digging a hole 4.5 m in diameter and 1.0 m deep. That's roughly 15 m3, which will be 30 tonnes or so. You'll need a skip holding 20 m3, perhaps more depending on the soil type.

@cougar - yes typo on my part, I meant m3.

Dig out half the volume and build up the side as to create he rest of the volume. No skip required.

Then when you are done tramploining you can chuck loads of foam pieces in for jump practice.

Nice in principle josh but that would mean the trampoline is above the ground, increasing the danger if a kiddie were to bounce off the side. I may do what I've seen elsewhere and fit the trampoline at ground level but build a doughnut shape around it with soil, then either plant this up or turf it. That way if they bounce off they're hitting the ground sooner/slower and it also acts slightly to hide the thing from view.

Why not just get a one with nets?

There are two methods we use in the construction method for calculating the volume of an irregular solid.

[i]Method 1 - Science![/i]

Only carried out by hardcore civil engineers and bewildered college students.

The volume is closely approximated using mathematical formulae, either the Trapezoidal Rule or Simpsons Rule.

The resulting volume is then increased by a bulking factor dependent on the type of soil.

Trapezoidal Rule - Tn=2h(y0+2y2+2y2++2yn?2+2yn?1+yn)

Simpson Rule - Sn=3h(y0+4y2+2y2+4y3++4yn?3+2yn?2+4yn?1+yn)

[i]Method 2 - Quantity Surveying[/i]

Quickly calculate the volume of the box which would surround the excavation, in your example D1 x the diameter of the pit.

Order a skip that size.

If it turns out not to be big enough, order another one.

Why not just get a one with nets?

[edit: and you don't have to dig an effing big hole and pay good money for a skip to take away the soil you may well want back one day 😉 ]

If it turns out not to be big enough, order another one.

And this, kids, is why analysts need to add contingencies to their numbers because no-one trusts the QS 😀

It will be a lot of soil! What will you fill the hole with once the kids get older/bored? A pool?

And for reference, the two most serious trampoline accidents I have come across were both on ground level (two broken legs in one accident due to mismatch in weights, and a serious compound fracture of the arm in another). Personally, I wouldn't bother now. And we had a 15 foot jumpking with full cage and frame for our teens.

If everything we did was totally safe I doubt we'd manage to cope with life in a few generations time.

I always assume the volume goes up to 11.

And this, kids, is why analysts need to add contingencies to their numbers because no-one trusts the QS

does the QS have to discount their numbers to account for an anticipated "just in case" factor? 🙂

Mrs Dubs teaches trampolining on the full size jobbies. She wouldn't consider having one in the garden without nets, sunken or not...

Basically, children are idiots at the best of times, even more so when they've been jumping around 😛

does the QS have to discount their numbers to account for an anticipated "just in case" factor?

We always have something spare tucked away. We don't like to talk about it.

Mrs Dubs teaches trampolining on the full size jobbies

I'd be wearing wellies for that.

If everything we did was totally safe I doubt we'd manage to cope with life in a few generations time.

If everything we did was totally safe I doubt we'd manage to cope with life in a few generations time.

Maybe not, but don't imagine you're even completely eliminating risk with nets on a trampoline. What you are doing is getting rid of unnecessary levels of risk.

If you want to do "natural selection" then over long enough the "trampolining without nets" gene will probably die out.

Mrs Dubs teaches trampolining on the full size jobbies

Shite career.

If everything we did was totally safe I doubt we'd manage to cope with life in a few generations time.

So why are you digging a huge hole?

A friend did just this - dug by hand to create a safe(r) environment for his autistic daughter. From his experience of doing it, I wouldn't recommend it to anyone unless they have access to machinery.

johndoh - Member
A friend did just this - dug by hand to create a safe(r) environment for his autistic daughter. From his experience of doing it, I wouldn't recommend it to anyone unless they have access to machinery.

My arms are machines 😉

A few safety Steves on here today... have fun!

A few safety Steves on here today... have fun!

I’m lost. Just why are you digging this hole again?

I think you misunderstood then described what i was suggesting

Drac - Moderator
I’m lost. Just why are you digging this hole again?

A sunken trampoline... so we don't have a huge 10ft high monstrosity taking up the garden. Also, kids play a lot more on ground trampolines than enclosed normal ones as it's instant access rather than going up ladders.

joshvegas - Member
I think you misunderstood then described what i was suggesting

You're talking about a basic version of the first picture...I'm thinking of the second. Is that right?

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Mrs Dubs teaches trampolining on the full size jobbies

Shite career.

Not as shite as digging holes.

It still takes up space though and kids really don’t care about using a ladder.

So it’s not about decreasing the danger of bouncing off the sides, it’s about digging a huge hole somehow makes the trampoline defy the laws of physics.

How awful to be concerned with safety - hang on, just need to make sure the kids cleaning underneath the looms aren't getting in the way...

Safety is another conversation though... come on laddie, stay on topic!

kids play a lot more on ground trampolines than enclosed normal ones as it's instant access rather than going up ladders

Evidence for this assertion? Ours gets played on lots despite the ladders, though we also have other ladders on a climbing frame - kids like ladders.

As an aside (again, due to my experience of knowing someone with one) I find them very odd. As they are at ground level there doesn't seem a need to walk around them but it feels equally odd to walk over them. I don't know why, it just feels unnatural.

EDIT: You could also have a ground level climbing frame where all the parts are just laid out on the lawn hereby negating the need for any climbing on the climbing frame.

My niece broke her leg on a trampoline without even falling off it. Just landed awkwardly on the bouncy bit.

Has the OP considered a swing? 😉

Took our two to one of them massive indoor trampoline parks yesterday, eldest is nursing some injuries today. Looked a right laugh though, going to try and go on with them next time.

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You can use a safety net with a recessed trampoline.

Consider using the spoil to landscape part of the garden, as eventually you likely to want to refill the hole...

Has the OP considered a swing?

Are you suggesting a ground level one, or should the OP dig a hole deep enough to hide the top of it?

aracer - Member
Evidence for this assertion? Ours gets played on lots despite the ladders, though we also have other ladders on a climbing frame - kids like ladders.

Googling! And my own thought process/knowing my kids.

Are you suggesting a ground level one, or should the OP dig a hole deep enough to hide the top of it?

Swing should be in a half pipe to maintain a constant distance between swing and ground.

We've got the swing... I built one with a 10ft high cross bar, slide and 2 swings earlier in the year 🙂 My favourite game is to see if I can push the kids fast enough on it for them to make a whistling sound as they speed through the air

Your kids are scared of ladders? Are you sure a trampoline is the thing for them?

Ah, now I understand, the trampoline is going in front of the swing, so they can jump off the swing onto the trampoline?

Scared? No...L.A.Z.Y!

In which case can I recommend a hammock instead

You should build a treehouse next....

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Ah i see what you mean.

Have you considered that you're digging a big pond?

Yes, mitigated with a sump at the bottom. If it pools I'll chuck a wee pond pump down there.

If it pools I'll chuck a wee pond pump down there.

Should probably tell kids it's not ok to wee under the trampoline.

😛

I'd prefer that to the places they're peeing in at the moment!!!

Pretty much filled the 8 yard skip, along with some of the other rubble lying around the garden. Though the 100cm deep hole plan was thwarted by a clay drainpipe right in the middle of the hole at 70cm deep, forcing the spec to be changed to a slightly raised trampoline with a nice grass banking! 🙂

Looks great though. Thanks for the maths.