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"The Engineer" - this month's problem

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Cycling Equipment
Published
24 March 2003
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26 March 2003
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Vic
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  1. 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.

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

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

    Quoted message said:

    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

  3. Quoted message said:

    I await next month's issue with baited breath!

    Quoted message said:

    Vic.

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

    --
    Ted Bennett Portland OR

  4. Ted Bennett said:

    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 hidden]

    Quoted message said:
    Quoted message said:

    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.

  5. Mark McMaster said:
    Quoted message said:

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

    Quoted message said:
    Quoted message said:

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

    Quoted message said:

    My answer: The average tension decreases.

    Quoted message said:

    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 <counter.li.orgcounter.li.org

  6. Quoted message said:

    "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

  7. Victor Papanek said:

    "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."

    Quoted message said:

    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 hidden] Palo Alto CA

  8. Quoted message said:

    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 <counter.li.orgcounter.li.org

  9. Ted Bennett <[email hidden]> wrote in message
    news:<[email hidden]>...

    Quoted message said:
    Quoted message said:

    I await next month's issue with baited breath!

    Quoted message said:

    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.

  10. Mark McMaster <[email hidden]> wrote in message news:<[email hidden]>...

    Quoted message said:
    Ted Bennett said:

    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 hidden]

    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.

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

    Quoted message said:

    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...

  12. [email hidden] wrote in message news:<[email hidden]>...

    Quoted message said:
    Victor Papanek said:

    "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."

    Quoted message said:

    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).

    Quoted message said:

    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...

    Quoted message said:


    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.

  13. "John Tserkezis" <[email hidden]> wrote in message
    "]news:[email hidden]...

    Quoted message said:
    Quoted message said:

    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).

  14. Dave Kahn said:
    Quoted message said:

    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.

    Quoted message said:

    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 <counter.li.orgcounter.li.org

  15. "John Tserkezis" <[email hidden]> wrote in message
    "]news:[email hidden]...

    Quoted message said:
    Dave Kahn said:
    Quoted message said:

    My answer: Stan falls flat on his backside. This is a rear wheel.


    The

    Quoted message said:
    Quoted message said:
    Quoted message said:

    centre of the hub is not where the rim is centred, but offset to one


    side to

    Quoted message said:
    Quoted message said:
    Quoted message said:

    make room for the gear cluster. The drive side spokes, due to their sharper angle, have to
    be at a


    higher

    Quoted message said:
    Quoted message said:
    Quoted message said:

    tension than the non-drive side.

    Quoted message said:

    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?

    Quoted message said:

    If one wants a specific answer, it's best they ask a specific question. Till then, every one of


    us

    Quoted message said:

    will give an answer that lines up with our interpretation of said vague


    question.

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

  16. W K said:
    Quoted message said:

    It could be a penny farthing for all we know.

    Quoted message said:

    With 16 spokes?

    Well, he DID say rear wheel...

    Quoted message said:
    Quoted message said:

    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.

    Quoted message said:

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

    (grin) Your point being?

    --
    Linux Registered User # 302622 <counter.li.orgcounter.li.org

  17. W K said:
    Quoted message said:

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

    Quoted message said:

    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.

    Quoted message said:

    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 <counter.li.orgcounter.li.org

  18. "George F. Johnson" <[email hidden]> wrote in message
    "]news:[email hidden]...

    Quoted message said:

    Wait a minute, aren't we making this a bit more difficult than it actually


    is?

    Quoted message said:

    I'm a mathematician and not an engineer so perhaps I'm missing an


    important

    Quoted message said:

    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

    Quoted message said:

    in each spoke, then it's an easy vector analysis (i.e. trig) problem to


    figure

    Quoted message said:

    each spokes tension. Sorry, I'm not going to compute each tension; I'll


    use

    Quoted message said:

    the familiar mathematician's gambit "the solution is intuitively obvious


    to the

    Quoted message said:

    most casual observer".

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

    Tim.

  19. George F. Johnson said:

    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.

    avocet.comwheelbook.html

    Quoted message said:

    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 hidden] Palo Alto CA

  20. whitfit said:
    Quoted message said:

    "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 (_)/ (_) |

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