Maths Headscratcher

[Steve Macluskie]

Here's a question for any mathematical genious out there.

 

Theoretically.......

 

I have a tallescope extended to a working platform height of 6m. I cant get the outrigger in place due to the restictions of the set so I place wee Johnny at the side of the 'scope to "brace it", he diligently holds the side of the scope, his hands at at 1.5m. Meanwhile big Brian (13 stone or 83kg) climbs the 'scope and starts fiddling about with some lights.

 

The maths/physics question is....

 

If big Brian overstretches and starts to topple the 'scope sidewayswhat force will wee Johnny have to exert at the bottom to keep big Brian from having a close encounter with the floor.

 

Fairly simple level calculations seem to suggest that the practice of having people bracing the scope is purely aesthetic and that wee Johnny would be joining big Brian in casualty.

 

Any thoughts suggestions or comments welcome

 

Any maths/physics genious's explanation even more welcome

 

Steve

[Thirdtap]

'Lo

Not answering your question just another related topic.

Not sure if I want find out answers to this question but, has anyone actually had an experience of an outrigger working or not working?

I have used outriggers on a scaff tower. The guide line for the tower stated - the brace was fixed tightly and out at 90' to the main body of the tower. The foot was to be positioned 1" off the floor.

If an accident occured the tower being on wheels surely would tip over, just maybe slower even with the braces used properly?

;)

[Bryson]

...dusts off rarely used Physics and Applied Mathematics A-Level...

 

If we assume that:

 

EDIT Big Brian has changed his name to Big Dave by Deed Poll

The weight of the tallescope is negligable. (It isn't, but calculating it in would require calculus)

Big Dave and Wee Johnny both weigh 83kg (For convenience: adjust calculations to suit..)

The Tallescope is rigid.

The tallesope has negligable width (again, for convenience)

Wee Johnny and Big Dave have all their mass at a single point in the centre of their bodies...

The base of the tallescope is a fixed point - ie - it can't slip sideways - (maybe Massive Jim is bracing that side?)

We ignore the additional complications of dynamic load.

 

 

Wee Johnny can probably apply a force 1.5m from the bottom equal to, say 30% of his body mass. So:

 

83 x 0.3 = 24.9N

 

and he is 1.5m from the fixed point, so has 1.5m of leverage:

 

24.9 x 1.5 = 37.35N

 

Big Dave is a mass of 83kg, concentrated 7m from the fixed point. With the tallescope level, he applies no sideways force - all the force is downwards. As the tallescope tips from the level, he applies sideways force in proportion to his angle from the vertical - ie, when he hits 90 degrees, all his force is going sideways (he has also just hit the floor, but we'll ignore that extreme case for now...) For convenience, we'll use Gradians rather than degrees (there are 400 gradians in a circle, not 360 - this means that each Gradian from the vertical he goes, that's another 1% of the force he creates going sideways. 1 Gradian = 0.9 degrees)

 

So he is 7m from the fixed point, and his angle of tilt (in gradians) is x, he weighs 83kg so, force applied:

 

Weight * percentage of force going sidways * leverage = Force applied

83kg * xGrad/100 * 7 = Force.

 

We know that Wee Johnny is in trouble when Big Daves sideways force exceeds 37.35N

 

So

 

83 * X/100 * 7 = 37.35

581* X/100 = 37.35

581X = 3735

x = 3735/581

x = 6.42Grad

6.42Grad = 5.778 degrees

 

So: Wee Johnny can survive the Tallescope going about 5 degrees off the vertical. In the real world - once you consider the weight of the tallescope itself, and the dynamic load on the end of it, that's probably more like 4 degrees of safety.

 

Remember: until it hits 4 degrees or so, Wee Johnny can apply enough force to return the tallescope to 0 degrees. 4 degrees is a noticeable tilt, so if it happens slowly enough, Johnny should be able to correct it...it's only when Johnny stops paying attention or Dave causes the tilt rather quickly that there's going to be a problem.

 

Still, outriggers are preferable...and don't hover them 1" off the floor, or they may fold in on themselves. Make contact with the floor, and lift them to move the scope. You can do that while the bloke at the top climbs back down... ;)

 

 

 

Hope this makes sense...If you think I'm wrong, let me know...it's been a while since I used these skills...

 

If anyone has a better way of estimating the force Wee Johnny can apply, that would help...30% was a kind of arbitary figure....

[Tom]

What if Wee Johnny is standing on the base of the scope - therefore applying his full force/weight in a downwards direction? Obviously once the thing starts to go there is nothing to stop it but surly there will be less chance of it going in the first place.

 

Also - shouldn't it be Wee Johnny up the scope and Big Dave doing the bracing.

[Ben]

Well the maths is correct.

 

If Wee Johnny is standing on the base of the scope - therefore applying his full force/weight in a downwards direction then in effect his mass is added to the total mass of the tallescope.

It is the distance from the centre of gravity of the tallescope that defines them as separate masses for the sake of the equation, therefore if he were on the base there would be no distance from the centre and you may as well just weigh down the bottom of the scope with weights. This would by the way make it much safer as it would to a point self right and would be much harder to tip in the first place. The more weight downwards on the bottom of the scope the further it could tilt and still rectify itself, just something to think about there.

ahhh, the joys of A level maths and physics, and I only finished them last year...

 

;)

[Steve Macluskie]

Hang on......

 

Who's big Dave? and what happened to big Brian?

 

You cant just swop round jobs like that, for all I know big Dave hasn't had his "introduction to tallescope" training yet.

 

;)

 

Steve

[gareth]

Remember: until it hits 4 degrees or so, Wee Johnny can apply enough force to return the tallescope to 0 degrees

... following which momentum kicks in, and the 'scope continues to tip in the other direction ... ;)

[Bryson]

... following which momentum kicks in, and the 'scope continues to tip in the other direction ...

 

No no no - Massive Jim, who has infinite mass, is bracing that side... ;)

Seriously, though...if Wee Johnny catches it in time, he should be able to apply the force in a controlled manner...

 

(PS: If anyone is looking for the discussion of common names, it's in the General section...)

[Ben]

well, from a physics point of view its a better idea for Massive Jim to put a vertical force onto the side that is lifting as the vertical force would be coupled with the natural gravity and would require less force to be applied than if Wee Johnny was to apply a horizontal force in order to rectify the tilt.

 

although the best way to do it is to attach 2 ropes to the basket at the top and use them to rectify the tilt from a distance, there would therefore be no risk of the second person gettign hurt if the worst happens and the scope tips over. the ropes are used in a similar way to tension coards meaning that not only would the tilt be rectified but the rope on the other side could be used to control the scope to an even landing. if of course the cables were at a fixed distance away from the centre of the scope and were taught, there is no risk of the scope tilting in the first place unless the rope/cable breaks...

but I guess that this would require more time (well about as much as out riggers) but the advantage over outriggers is the force is pulling the cables outwards as opposed to out riggers which are pushed inwards and can therfore buckle, that cant happen with suspension cables.

 

but I have gone way off the point here which is:

its a better idea for Massive Jim to put a vertical force onto the side that is lifting than for Wee Johnny to apply a horizontal force in order to rectify the tilt as it would need less force.

[Thirdtap]

So what has happened since I was last here?

Wee Johnny is still ever alert at the bottom of the scope and Massive Jim has come back from a cig break outside the dock door.

At which point in this story is Anne from accounts going to authorise funds for new access equipment? ;)

[peter]

Anne from accounts comes just as Fred the Flyman performs cue 65 in which Paul the Pig is flown from SL to SR.

[Ben]

Anne from accounts will only authorise funds for new access equipment when it has been proved that the old equipment is missing, the job has been carried out and the new equipment is deemed the minimum requirement, and even then we will have to wait till the next financial year...

[Stu]

Well, looks like it's time to conviently 'lose' the scope, and convince Anne from Finace to buy a nice Genie, seeing as it's 3 weeks til the new financial year!

 

Woopee!

 

Stu

[Thirdtap]

'lose' the 'scope?

Put it outside the dock chained up? The thicker the chain the quicker it will go.

Or turn it into a wicker man and sell it to some hippies or tourists?

 

Really though... I looked at genie lift prices recently and was quite suprised and the prices. I got quotes for I think a 25foot version and they ranged from £9K from high street hire shop to around £5K + VAT from a rigging company. If people feel that tallescopes while handy aren't going to be suitable in the future, plans have to made to get for alternative access equipment for your venue. I am sure most people would do this in an instant IF the money was available. The big question is how to get this money?

;)

[peter]

You could always go round the loading doors of theatres up and down the country, with a set of bolt cutters, and start up a second hand tallescope business?