"The Engineer" - this month's problem

[Vic]

I occasionally read "The Engineer", which is a UK technology rag posted out free, and supported by
the adverts which fill about 50% of its pages.

Each month there's a prize question, ostensibly on a topic which may be of interest to engineers,
but more usually of the fox-chicken-grain type.

This month's question caught my eye, because I wonder just how many of the magazine's readership
will get it right, and if even the composer of the problem will have the answer right...

"Stan the cyclist is keen to stay abreast of latest developments so purchased a hi-tech carbon fibre
rear wheel with 16 radial spokes equally spaced and alternating eight to each side of the hub. The
wheel builder has centred the rim and trued the wheel and then torqued up the spokes to give a
tension of 125kg (sic) per spoke. As Stan lowers his 75kg onto the saddle he wonders what the
tension is in the spokes now."

I await next month's issue with baited breath!

Vic.

 

[Ted Bennett]

I have no doubt that this will get the fur flying, Vic!

My answer: The average tension of all the spokes is unchanged.

> I occasionally read "The Engineer", which is a UK technology rag posted out free, and supported by
> the adverts which fill about 50% of its pages.
>
> Each month there's a prize question, ostensibly on a topic which may be of interest to engineers,
> but more usually of the fox-chicken-grain type.
>
> This month's question caught my eye, because I wonder just how many of the magazine's readership
> will get it right, and if even the composer of the problem will have the answer right...
>
> "Stan the cyclist is keen to stay abreast of latest developments so purchased a hi-tech carbon
> fibre rear wheel with 16 radial spokes equally spaced and alternating eight to each side of the
> hub. The wheel builder has centred the rim and trued the wheel and then torqued up the spokes to
> give a tension of 125kg (sic) per spoke. As Stan lowers his 75kg onto the saddle he wonders what
> the tension is in the spokes now."
>
> I await next month's issue with baited breath!
>
> Vic.

--
Ted Bennett Portland OR

 

[Ted Bennett]

> I await next month's issue with baited breath!

> Vic.

I just noticed the use of "baited" rather than "bated breath" which clearly suggests a troll. Heh.

--
Ted Bennett Portland OR

 

[Mark McMaster]

Ted Bennett wrote:
> I have no doubt that this will get the fur flying, Vic!
>
> My answer: The average tension of all the spokes is unchanged.

My answer: The average tension decreases.

The sum of the tension decreases in the load affected zone at the bottom of the wheel is greater
than the sum of all the (small) tension increases elsewhere in the wheel.

Mark McMaster [email protected]

>
>
>>I occasionally read "The Engineer", which is a UK technology rag posted out free, and supported by
>>the adverts which fill about 50% of its pages.
>>
>>Each month there's a prize question, ostensibly on a topic which may be of interest to engineers,
>>but more usually of the fox-chicken-grain type.
>>
>>This month's question caught my eye, because I wonder just how many of the magazine's readership
>>will get it right, and if even the composer of the problem will have the answer right...
>>
>>"Stan the cyclist is keen to stay abreast of latest developments so purchased a hi-tech carbon
>>fibre rear wheel with 16 radial spokes equally spaced and alternating eight to each side of the
>>hub. The wheel builder has centred the rim and trued the wheel and then torqued up the spokes to
>>give a tension of 125kg (sic) per spoke. As Stan lowers his 75kg onto the saddle he wonders what
>>the tension is in the spokes now."
>>
>>I await next month's issue with baited breath!
>>
>>Vic.

 

[John Tserkezis]

Mark McMaster wrote:

>> I have no doubt that this will get the fur flying, Vic!

>> My answer: The average tension of all the spokes is unchanged.

> My answer: The average tension decreases.

> The sum of the tension decreases in the load affected zone at the bottom of the wheel is greater
> than the sum of all the (small) tension increases elsewhere in the wheel.

My answer: Stan falls flat on his backside. This is a rear wheel. The centre of the hub is not
where the rim is centred, but offset to one side to make room for the gear cluster. The drive side
spokes, due to their sharper angle, have to be at a higher tension than the non-drive side.

So, if Stan's magician wheel-builder actually managed to get the wheel to sit still, it would be
so unstable that it would be useless.

Or am I missing something, I've only every relaced a wheel three times in my life, I'm no pro.

--
Linux Registered User # 302622 <http://counter.li.org

 

[Peter]

> "Stan the cyclist is keen to stay abreast of latest developments so purchased a hi-tech carbon
> fibre rear wheel with 16 radial spokes equally spaced and alternating eight to each side of the
> hub. The wheel builder has centred the rim and trued the wheel and then torqued up the spokes to
> give a tension of 125kg (sic) per spoke. As Stan lowers his 75kg onto the saddle he wonders what
> the tension is in the spokes now."

It would have to be something simple like divided weight of cyclist by the number of spokes and add
the amount to each spoke which would be
75/2/16=2.3kg and you get a tension of 127.3kg/spoke.But of course it would probably be a rotary
tension shifting with the rotation of the wheel.Therefore at rest with no weight added the
tension /spoke would be 175kg.When Stan sits on the bike who weights 75kg which adds 37.5kg to
each wheel (That's if the the center of gravity is actually centred).Now when the spokes are at
the north,south,est,west position the tension on the spokes est and west are 125kg or pretty
close to 125kg (don't have the formulas for calculating the slight tension deflection).The
north spokes would be 125kg plus1/2 of 37.5=18.75 which would be 143.75 /spoke.For the south
spokes the tension would be 125kg/spoke minus 18.75=106.25.Then when the wheel rotates ....well
you can sit there and calculate the tension shifts for each point of wheel rotation on the
spokes. PeterM

 

[Jobst Brandt]

Victor Papanek writes:

> "Stan the cyclist is keen to stay abreast of latest developments so purchased a hi-tech carbon
> fibre rear wheel with 16 radial spokes equally spaced and alternating eight to each side of the
> hub. The wheel builder has centred the rim and trued the wheel and then torqued up the spokes to
> give a tension of 125kg (sic) per spoke. As Stan lowers his 75kg onto the saddle he wonders what
> the tension is in the spokes now."

> I await next month's issue with baited breath!

Do something about your halitosis first. Bait in your breath stinks. It needs abatement. Meanwhile,
all readers of "the Bicycle Wheel" are disqualified because that is where the answer(s) to the
question are found and the book is most likely the source of the question, this sort of thing being
unknown at the time of its publication.

Why did the author confuse the problem by using a REAR wheel as subject? The problem statement is
confusing because rear wheels do not have the same tension on left and right sides.

Jobst Brandt [email protected] Palo Alto CA

 

[John Tserkezis]

[email protected] wrote:

> Why did the author confuse the problem by using a REAR wheel as subject? The problem statement is
> confusing because rear wheels do not have the same tension on left and right sides.

That's the point. It's a trick question.

--
Linux Registered User # 302622 <http://counter.li.org

 

[Vic]

Ted Bennett <[email protected]> wrote in message
news:<[email protected]>...
> > I await next month's issue with baited breath!
>
> > Vic.
>
> I just noticed the use of "baited" rather than "bated breath" which clearly suggests a troll. Heh.

Nothing so subtle or contrived: The "baited" was a slip of the brain (ie. Until now, I wasn't even
aware of the difference and usages re: "baited" and "bated").

You must be a whiz with the cryptic crosswords, Ted!

Vic.

 

[Vic]

Mark McMaster <[email protected]> wrote in message news:<[email protected]>...
> Ted Bennett wrote:
> > I have no doubt that this will get the fur flying, Vic!
> >
> > My answer: The average tension of all the spokes is unchanged.
>
> My answer: The average tension decreases.
>
> The sum of the tension decreases in the load affected zone at the bottom of the wheel is greater
> than the sum of all the (small) tension increases elsewhere in the wheel.
>
> Mark McMaster [email protected]

I'd go along with this. It's about as good an answer as you can give, considering how the
problem is posed.

I'm primarily interested in:

a) The solution proposed by the problem composer.

and

b) What the readership of "The Engineer" make of the problem.

I'm thinking that the guy who composed the problem must be aware of the non-intuitive behavior of a
spoked bike wheel, because it gives a satisfying "Ahhh!" moment to the un-initiated when the
solution is revealed...

Vic.

 

[Dave Kahn]

John Tserkezis <[email protected]> wrote in message
news:<[email protected]>...

> My answer: Stan falls flat on his backside. This is a rear wheel. The centre of the hub is not
> where the rim is centred, but offset to one side to make room for the gear cluster. The drive
> side spokes, due to their sharper angle, have to be at a higher tension than the non-drive side.

Who said anything about a gear cluster? It could be a fixed wheel.

--
Dave...

 

[Vic]

[email protected] wrote in message news:<[email protected]>...
> Victor Papanek writes:
>
> > "Stan the cyclist is keen to stay abreast of latest developments so purchased a hi-tech carbon
> > fibre rear wheel with 16 radial spokes equally spaced and alternating eight to each side of the
> > hub. The wheel builder has centred the rim and trued the wheel and then torqued up the spokes to
> > give a tension of 125kg (sic) per spoke. As Stan lowers his 75kg onto the saddle he wonders what
> > the tension is in the spokes now."
>
> > I await next month's issue with baited breath!
>
> Do something about your halitosis first. Bait in your breath stinks. It needs abatement.

A previous poster beat you to it, but repetition does enhance recollection (for me, at least).

> Meanwhile, all readers of "the Bicycle Wheel" are disqualified because that is where the answer(s)
> to the question are found and the book is most likely the source of the question, this sort of
> thing being unknown at the time of its publication.

I doubt if the book is well known amongst the (mechanical) engineering community, who will form the
audience for the original problem. If it isn't in "Kempe's", then it probably doesn't matter...

>
> Why did the author confuse the problem by using a REAR wheel as subject? The problem statement is
> confusing because rear wheels do not have the same tension on left and right sides.

Who knows? Maybe it is simply a badly posed question, but if the presence of the hub was immaterial,
I suspect the composer would have referred to generic "bike wheels" rather than specifying the rear
wheel. Maybe we are supposed to assume it's a single-speed fixie?

On the other hand, no dimensions are given in the question, so it is impossible to account for the
hub on the basis of the information supplied.

All the same, I'll make sure I snag a copy of the next issue of "The Engineer" for the
published solution

Vic.

 

[W K]

"John Tserkezis" <[email protected]> wrote in message
news:[email protected]...
> [email protected] wrote:
>
> > Why did the author confuse the problem by using a REAR wheel as subject? The problem statement
> > is confusing because rear wheels do not have the same tension on left and right sides.
>
> That's the point. It's a trick question.

The OP wonders about that. I imagine many engineers will make assumptions like a completely stiff
rim - after all if you don't make such assumptions working out the precise behaviour of the rim has
to be rather tricky.

Perhaps it'll be an exercise in what assumptions you can and cannot make as an engineer.

(apart from all the more subtle stuff we don't know how much of his 750N goes on the back wheel).

 

[John Tserkezis]

Dave Kahn wrote:

>> My answer: Stan falls flat on his backside. This is a rear wheel. The centre of the hub is not
>> where the rim is centred, but offset to one side to make room for the gear cluster. The drive
>> side spokes, due to their sharper angle, have to be at a higher tension than the non-drive side.

> Who said anything about a gear cluster? It could be a fixed wheel.

It could be a penny farthing for all we know. If one wants a specific answer, it's best they ask a
specific question. Till then, every one of us will give an answer that lines up with our
interpretation of said vague question.

--
Linux Registered User # 302622 <http://counter.li.org

 

[W K]

"John Tserkezis" <[email protected]> wrote in message
news:[email protected]...
> Dave Kahn wrote:
>
> >> My answer: Stan falls flat on his backside. This is a rear wheel.
The
> >>centre of the hub is not where the rim is centred, but offset to one
side to
> >>make room for the gear cluster. The drive side spokes, due to their sharper angle, have to
> >>be at a
higher
> >>tension than the non-drive side.
>
> > Who said anything about a gear cluster? It could be a fixed wheel.
>
> It could be a penny farthing for all we know.

With 16 spokes?

>If one wants a specific answer, it's best they ask a specific question. Till then, every one of
us
> will give an answer that lines up with our interpretation of said vague
question.

Isn't that last sentence the definition of "engineer"

 

[John Tserkezis]

W K wrote:

>> It could be a penny farthing for all we know.

> With 16 spokes?

Well, he DID say rear wheel...

>> If one wants a specific answer, it's best they ask a specific question. Till then, every one of
>> us will give an answer that lines up with our interpretation of said vague question.

> Isn't that last sentence the definition of "engineer"

(grin) Your point being?

--
Linux Registered User # 302622 <http://counter.li.org

 

[John Tserkezis]

W K wrote:

>> That's the point. It's a trick question.

> The OP wonders about that. I imagine many engineers will make assumptions like a completely stiff
> rim - after all if you don't make such assumptions working out the precise behaviour of the rim
> has to be rather tricky.

True. Out of habit, I make the most complex assumptions, that way, the easy answers are easier.

> Perhaps it'll be an exercise in what assumptions you can and cannot make as an engineer.

Again, true.

There's only so much one can presume when faced with a vague answer. Best if one can actually
_look_ at it, that way, there's no mistake. I've been faced with a number problems from
clients with "impossible" symptoms simply because they've "forgotten" to mention some very
important details.

--
Linux Registered User # 302622 <http://counter.li.org

 

[Tim Cain]

"George F. Johnson" <[email protected]> wrote in message
news:[email protected]...
> Wait a minute, aren't we making this a bit more difficult than it actually
is?
> I'm a mathematician and not an engineer so perhaps I'm missing an
important
> principle of statics or something but it seems to me that if we're talking about total or average
> tension then the answer is no change. If it's
tension
> in each spoke, then it's an easy vector analysis (i.e. trig) problem to
figure
> each spokes tension. Sorry, I'm not going to compute each tension; I'll
use
> the familiar mathematician's gambit "the solution is intuitively obvious
to the
> most casual observer".
>

I thought that "The solution is left as an excercise for the reader".

Tim.

 

[Jobst Brandt]

George F. Johnson writes:

> Wait a minute, aren't we making this a bit more difficult than it actually is? I'm a mathematician
> and not an engineer so perhaps I'm missing an important principle of statics or something but it
> seems to me that if we're talking about total or average tension then the answer is no change.

Not so, because the rim is not infinitely rigid, and therefore, the age old easily dismissed
response to loads of bicycle wheels was misdiagnosed for more than a century. The tensioned wire
wheel does not work the way people believe. I am disappointed that even though "the Bicycle Wheel"
has been in print for about 20 years, these misconceptions are still widespread even among bikies.

http://www.avocet.com/wheelbook/wheelbook.html

> If it's tension in each spoke, then it's an easy vector analysis
> (i.e. trig) problem to figure each spokes tension. Sorry, I'm not going to compute each tension;
> I'll use the familiar mathematician's gambit "the solution is intuitively obvious to the
> most casual observer".

It may be easy but it is not what you surmise. Average tension decreases and as I have often pointed
out here on wreck.bike, the highest (average and total) tension in a bicycle wheel exists when the
bicycle is unloaded. There is an increase (and decrease) when braking while all other effects
produce negligible changes.

Jobst Brandt [email protected] Palo Alto CA

 

[David L. Johnso]

On Tue, 25 Mar 2003 09:42:04 -0500, whitfit wrote:

>> "Simplifying assumptions generously accepted!"
>
> Simplifying assumptions generously acceted... Hmmm... You must be an economist.

Or maybe another mathematician...

--

David L. Johnson

__o | There is always an easy solution to every human problem - neat, _`\(,_ | plausible, and
wrong. --H.L. Mencken (_)/ (_) |