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Design M.O.

  1. Sep 6, 2006 #1
    (This is rather long, so if you do not wish to read it all please scroll down to ‘The Problem')

    This is my situation:

    I am designing a powered-bicycle that will feature a two-wheel-drive capability. I need to calculate the diameter of the drive shaft that transfers power to the front wheel (it needs to be as small as possible).

    In order to calculate this diameter first I need to identify all of the resistive forces acting on the bike (to determine how much power will pass through it). So, to be able to do that I need to know how much the bike will weigh and how much power the components will absorb (mechanical loss).

    How would you go about doing this?

    How I went about doing this was to, concerning the estimated weight of the bike, look at other bikes, both motorcycles and bicycles. I looked at how much other bikes weigh and determined what the maximum weight of my bike will be by comparing the power of the motorcycles, that I looked at, to their weights, and also by noting the frame-weights of the bicycles, that I looked at (down hill mountain bikes because they are the strongest). I also noted the combined weight of the small engine I will use and also (because my bike will be a hybrid petrol/electric-powered design) the weight of the electric drive components (motor and battery). My conclusion was 50kg, which is the maximum I would want the bike to be, as it needs to be light enough to carry over fences and gates, etc., during long distance cross-country tours. Of course I factored into this 50kg estimation figure the materials I wish to use.

    Now that I know how much my bike will weigh I can calculate most of the forces acting on it. I know how big the bike will be and what sort of tyres it will use, so I am able to calculate the drag forces from the air and also from rolling resistance. I can workout how much force is required to propel the bike, with rider and cargo, up an inclined plane, I am able to workout how much force is needed to accelerate the bike (F = MA) and I am also able to calculate the rotational inertia of the wheels.

    I have in mind minimum performance figures (such as top speed, acceleration, etc) that the bike needs to be capable of, so I measured estimated forces up to these limits.

    This leaves the problem of trying to estimate the drag forces of the bikes’ drive components. I need to estimate the efficiency of bearings, drive shafts, drive chains, CV-joints (at varying angles), spiral bevel gears and one-way clutches. I have drag force figures for bearings and one-way clutches, although not at different speeds (the manufactures tend not to have this information) and not during acceleration (for acceleration I will calculate the rotational inertia for the individual components and calculate the force that way). Drive shaft efficiency is easy enough to calculate and, once I know the exact dimensions, spiral bevel gear efficiency, I hope, will be a straightforward calculation thanks to a formula I found.

    The Problem:

    Although I found a formula for calculating bicycle drive chain efficiency, I am not confident that I can use it properly. I do not know what units parts of the formula need to be expressed in and I am also not confident that I will be able to source the information, such as various coefficients of friction for parts of the chain, needed for the equation. Drive chain power-loss formulae are hard to come across, as are equations for CV-joint efficiency, to name just two drive components. Also, there is a possibility that my spiral bevel gear formula will prove impossible for me as well!

    So, what am I to do? I know that these drive components absorb power (cause a resistive force) but I have no accurate way of identifying exactly how much. Most mechanics people say a good drive chain that is well maintained will be about 98% efficient and spiral bevel gears should not be less than about 95% efficient (grease lubrication). Should I just use these figures in my force estimations? It does not seem very scientific to me; it seems to be making a guess based on hearsay!

    Until the bike is built this project is purely theoretical, and with little opportunity (at this stage) for conducting experiments with models, etc. I am writing-up how I went about this project, how I determined component (TWD drive shaft) dimensions and generally the fundamental mathematics involved in basic design work. I will be presenting this project to a university in an attempt to gain a place on a degree course in Engineering, and I do not have very much time at all to finish it (I currently have a place in the Foundation Year). The project (write-up) has to be scientifically based and it has to be of academic standard (albeit 1st year entry standard), so it cannot be based on guesswork.

    Would you just assume 98% for a drive chain, or 95% for a bevel gear? Is this how professional engineers would go about making an estimation (estimation, not guesstimation)? In the absence of available formulae, what other option do I have?

    What is the standard design modus operandi for such scenarios?
  2. jcsd
  3. Sep 6, 2006 #2


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    Despite the obvious intensive thought that you've put into this, you haven't mentioned what the motive power is. To start with, it's probably easiest to just stick with conventional chain drive. If you want to go with a driveshaft, something on the order of 1/4" diameter mild steel rod should be fine for anything under 3 hp. If you're planning on stuffing a 413 Wedge into it, then obviously you'd need to upgrade. We need more info.
  4. Sep 6, 2006 #3
    The question is really one that applies to any powered-engineering design project, from a buzz-board to a 3-story dump truck.

    I am using a drive shaft as a part of the two-wheel-drive system as the means of transmitting power to the front wheel to allow for steering and front suspension movement.

    The bike will have an internal main shaft that is connected to the rider’s pedals (via a human-powered gearbox), the petrol engine and also to the electric motor. This main shaft is directly connected to the rear wheel via a drive chain. Power is sent from the main shaft to the front wheel in a series of stages (robbing efficiency, which makes power-loss estimations all the more important). First the main shaft sends power to another parallel shaft (mounted internally at the front of the main body of the bike) using another drive chain. This second shaft transmits the power via a spiral bevel gearbox (this gearbox will provide the rider with three separate choices of ratios of drive between the front and rear wheels). The spiral bevel gears send the power out the front of the bike in a shaft perpendicular to the main and second shafts. This perpendicular shaft is connected to a CV-joint. The CV-joint is connected to a telescopic shaft, which then connects to a second CV-joint. That (the two CV-joints and telescopic shaft) takes care of front suspension movement. A third CV-joint (that I am still designing) will take care of steering movement and will be mounted where the front forks (Hossack type forks, not regular type) connect to the upper front suspension arms (wishbone) directly beneath the steering pivot. Another couple of drive shafts mounted onto the front forks, via another two sets of bevel gears, transmits power through the final stages before it reaches the front wheel (a spiral crown gear will be mounted to the front wheel via a one way clutch).

    The electric motor could be as powerful as 11kw. The petrol motor will only be 1.2hp. This forward TWD perpendicular drive shaft has to be as small as possible as I wish to use an internal gear change mechanism within the bevel gearbox (a slider mounted around the shaft changes ratio by sliding through the driven spiral gears). I do not wish to digress too much away from the main question I posed within this thread, but I am guessing that I can make this shaft smaller by making it turn faster. I.e. the faster it turns the lower the torque it will have to cope with, ergo it will not need to be so large?
  5. Sep 7, 2006 #4


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    This thing is way more complicated than I expected. I didn't even know that bicycles have suspension these days. (I haven't ridden one in 35 years.) There are so many combinations and variables here that you might just have to trace the power through every one individually and calculate at each point. Out of my league, but others will be able to help. Keep us posted about your progress; it sounds very interesting.
  6. Sep 10, 2006 #5


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    the idea has been tried before none had any real impact, the only multi drive system with MBs is a side car drive.
  7. Sep 11, 2006 #6
    By 'MBs' do you mean 2WD? If so, a few have had commercial success and recently a 2WD system has been used in a Dakar (prob' wrong spelling) dirt bike.

    Commercial success is one thing; success as a machine and off road transportation device is another. And it is the latter that I care about.
  8. Jan 4, 2007 #7
    Well, at the moment I am busy with a 3 wheeled HPV. 2 wheels in front en 1 rear wheel. And I have a diffuculties with my powertrain. I want to use the CV-joints, but I don't know wether there available that small. This is maybe a bit off topic. But perhaps you know a retailer who sales cv joints?


    The cv-joint must connect the red parts

    Attached Files:

  9. Jan 23, 2007 #8
    I know of no source for sub-auto sized CV joints. If I am unable to locate a suitable supplier / manufacturer I will have to make my own.
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