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Old 03-03-18, 03:53 PM
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For you Nerds

Something for you Nerds (with a capital N). I was curious about the effect of bumps on a bike's behavior so I did a little experiment and spent some time mulling over the data. It was informative and surprising.

There is a marvelous little device called Pocketlab (thepocketlab.com) which contains a whole bunch of sensors, including 3-axis accelerometer which has a range +/-6g's and a resolution of 0.008g. It can run for 8 to 12 hrs on its internal rechargeable battery and talks to a smartphone via Bluetooth. So I acquired a Voyager model and attached it to the fork of the '87 Bianchi Brava that I use for much of my commuting.



Then I recorded parts of my commute at its highest data rate 50 samples/sec (20msec). Depending on the terrain I ride between 10 and 20mph; 10mph is about 9mm/sec so the spatial resolution longitudinally isn't good enough to measure the shape of the response to most bumps. That's a messy problem (see below) and also what I'd really like to see, so I may try this again riding much slower. I also recorded distance to the ground using its IR rangefinder which has a resolution of 1cm, but it didn't show much interesting.

Here are some interesting graphs (created with OpenOffice). Most show vertical (orange) and longitudinal (blue) axes; a few show all three axes, vertical, longitudinal, and lateral. You can identify the vertical because its average is -1g instead of 0, with a negative sign because the sensor was pointing down for the rangefinder.

First a large-scale view of what appears to begin with waiting at a stoplight. It's easy to see when I was moving in the last third. It appears that I let the handlebar flop to one side while stopped because the lateral (orange) and vertical (gray) lines are not at their normal at-rest positions, -1 and 0 respectively.



Here is a stretch of bumps about 3sec long. The details of the last bump (starting about data point 120) are especially interesting.



First, the downward pulse in the vertical line (orange) means I hit a raised bump rather than a dip. (Remember, the sensor's Z axis was pointing down.) The vertical stress exceeded 3g's, a pretty high number though not unusual.

The longitudinal curve is surprising. The upward peak means the axle accelerated forward, not backward, and the magnitude also exceeded 3g's! It then decelerated and eventually settled down to its background oscillation (which we will discuss later). So you have to ask, how can hitting a bump shove the axle forward?? And by that much! Surely I didn't stomp on the pedals to accelerate that hard, impossible since the rear tire won't sustain that much grip with the road.

The answer is in the fork geometry. Look at this slightly exaggerated picture.



The thrust line of a bump's force can only be radial, i.e. on a line running through the axle. Depending on the height of the bump that line may project to the headset above or below the lower bearing race which acts as a fixed location. If the line projects above the headset then the force of the bump will be to bend the fork upward, pushing the axle forward. The headset itself experiences an impulse backwards even greater, so the bike will be slowed. There is one height at which the axle experiences no longitudinal impulse at all.

Consider some numbers: For a hypothetical 350mm radius and HT angle 73deg with no rake, the thrust at first contact with 1.53cm bump goes through bottom of headset (HS). The thrust angle (TA) would be the HT angle, 73deg. A bump smaller than this will always deflect the fork forwards as the fork bends in an arc centered at HS. A real bike has a rake of, say, 4.5 to 5cm. This means the first contact with a 3.3cm bump goes through HS, for a TA of about 65.0deg.

If the headset does not move upward in a bump, i.e. remains at the same height, the maximum thrust will always occur when the axle is directly over the bump (DOB), i.e. 90deg TA. Actual behavior is complicated as it depends on the bike speed w.r.t. the spring rate of the fork accelerating the mass of the bike and rider upward. A slower bike speed means more upward movement of the HT (normalized for the lower impact), effectively moving the centroid of the thrust point forward toward first contact as the tire deflection diminishes through the course of the bump over what it would have been were the HT not moving vertically. On a typical bike maybe 1/3 the mass of bike and rider are over the front wheel, but wheel and fork together are significantly less. So for a short duration bump event a stationary HS is a reasonable talking point.


Regardless of the speed, the first significant movement of the axle will be somewhere between first contact (65deg TA) and DOB (90deg TA), and the first detectable acceleration of the axle will occur as soon as the tire has deformed enough that the contact patch has moved forward. Thus any bump smaller than about 3.3cm will deform the fork so as to push the axle upward and forward even though the thrust at the HS will be upward and backward. In principle we can detect whether a bump in this data was taller than 3.3cm by whether the longitudinal acceleration was forward or backward. Both types are visible in the data. Here is another example.



In this example the fork is knocked forward by the bump at data point 24, rebounds by decelerating a lot as the movement of the bike upward unloads the weight from the fork, then accelerates forward again as the weight falls back down to flex the fork forward.

This example shows the bike hitting a dip. It briefly releases the load on the front wheel of the rider's weight, and this allows it to move backwards w.r.t. the bike. When the tire hits the upward slope on the far side of the dip it knocks the axle forward again by flexing the fork forward and up.



Finally, note how the background movement seems to involve a consistent up/down or forward/backward acceleration. This suggests a forward/backward resonance of the fork. the fact that it changes direction on every data point suggests that it is close to the Nyquist frequency, in this case 25Hz. I picked up the bike and thumped downward on the front wheel and obtained this pic.



The pattern isn't quite every other point though. So I thumped the wheel while measuring the frequency with Kewlsoft's accelerometer and came up with about 17Hz. So the fork is quietly resonating when driven by the random noise of pavement irregularities.
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Old 03-03-18, 04:18 PM
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Jim,
Are you planning to audition for a part as a professor on Big Bang Theory?

Actually it is very interesting data, and I will try to put my dormant high school physics to work. Thank you for sharing Jim.
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Old 03-03-18, 04:35 PM
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Interesting.
I guess where I would want to take this would be to instrument the fork ( essentially at the axle) and say the top tube immediately aft of the steerer. To get a feel for the absorption of the fork.
There were the bike shop mechanic arguments about how quick the radius of the fork is related to road feel, then there are additional arguments over straight blade forks...
And my personal observation of twin plate crown forks vs "box" crown units.
Then the whole can of worms regarding tire cross-section and pressure and rolling resistance...
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Old 03-03-18, 04:42 PM
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@jimmuller, Sharon needs to find a new project for you to do. This is way above my seminary pay grade!
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Old 03-03-18, 04:44 PM
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My head hurts now

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Old 03-03-18, 04:45 PM
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This was appreciated..cool bit of info. Now it would be interesting to do the same with a bike you consider the best rider and note the different resonances in the sine wave. It would be kinda hard to do everything in a controlled environment, unless you were using a lab with consistent variables for each.
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Old 03-03-18, 05:07 PM
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Originally Posted by repechage
Interesting.
I guess where I would want to take this would be to instrument the fork ( essentially at the axle) and say the top tube immediately aft of the steerer.
Thanks. Instrumenting both the axle and HS was my original intent, but I'd have to buy a second Pocketlab (it was whimsical enough to buy this one) and also synchronize their data manually in OpenOffice or Excel. Maybe... The problem is, 50Hz sample rate isn't quite fast enough for what I'd really like to see.


Originally Posted by dunrobin
Now it would be interesting to do the same with a bike you consider the best rider and note the different resonances in the sine wave. It would be kinda hard to do everything in a controlled environment, unless you were using a lab with consistent variables for each.
That is the hard part. I can measure the response of the fork here at home with my phone, but not while riding. I suspect the Bianchi is pretty representative though the decay rates and resonant frequencies would vary bike to bike. Some of my bikes don't have mounting holes on the fork.

A different approach would be simply to compare oscillation frequencies and bump rapidity on the road. Running the same stretch of road at exactly the same speed would be tough though.

But this shows why road tests like riding down a set of speed bumps is so meaningless. Real roads don't have such continuous equally-spaced bumps. And no matter what the bump spacing, the bike's response and the rider's speed and weight will affect how the fork oscillation sets up in phase w.r.t. the bumps. Maybe I'll try it. Don't hold your breath though.
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Old 03-03-18, 05:21 PM
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Very cool!

I would donate $20 to the fund to purchase a 2nd device so you could continue the tests for the forum. That would be worth it for the discussions it would generate.

Originally Posted by jimmuller
Thanks. Instrumenting both the axle and HS was my original intent, but I'd have to buy a second Pocketlab (it was whimsical enough to buy this one) and also synchronize their data manually in OpenOffice or Excel. Maybe... The problem is, 50Hz sample rate isn't quite fast enough for what I'd really like to see.




That is the hard part. I can measure the response of the fork here at home with my phone, but not while riding. I suspect the Bianchi is pretty representative though the decay rates and resonant frequencies would vary bike to bike. Some of my bikes don't have mounting holes on the fork.

A different approach would be simply to compare oscillation frequencies and bump rapidity on the road. Running the same stretch of road at exactly the same speed would be tough though.

But this shows why road tests like riding down a set of speed bumps is so meaningless. Real roads don't have such continuous equally-spaced bumps. And no matter what the bump spacing, the bike's response and the rider's speed and weight will affect how the fork oscillation sets up in phase w.r.t. the bumps. Maybe I'll try it. Don't hold your breath though.
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Old 03-03-18, 06:36 PM
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Could this be used to compare ride quality of two different tires? How about to measure flex of a frame?
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Old 03-03-18, 07:06 PM
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I wish I had enough 'little gray cells' and education to follow the discussion but those of you with this capacity should should get a copy of Bicycling Science from MIT press for much more of the same. This thread would likely be a worthy entry in the book. I enjoy it even as a layperson. Frame materials, rolling resistance, it's all in there.
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Old 03-03-18, 08:01 PM
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I'm only a nerd (little n), so ya lost me.


But at least it sounds like you enjoyed the experience.
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Old 03-03-18, 08:05 PM
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Originally Posted by clubman
I wish I had enough 'little gray cells' and education to follow the discussion...
You're in good company; I was wandering-around-lost by his second paragraph

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Old 03-04-18, 02:10 AM
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tl,dr

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Old 03-04-18, 03:38 AM
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I will have to read this again when it's not 1:30 AM, but I like what you are doing and analyzing here. Resonant frequencies of various steels, to say nothing of putting this on vintage aluminum forks (Cannondale et al) or carbon-fiber. I would imagine, given my experience with steel and aluminum in this context, that aluminum will give a higher frequency, or at the very least, a more rapid response/oscillation.
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Old 03-04-18, 04:21 AM
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Interesting. I presume you’ve heard of the International Roughness Index pertaining to roadways?


https://en.m.wikipedia.org/wiki/Inte...oughness_Index
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Old 03-04-18, 06:47 AM
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When explaining anything to me, beyond thingamajig, whatchamacallit, doodad, thingamabob,and doohickey, it becomes too technical for me. But thanks for the effort.
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Old 03-04-18, 07:56 AM
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Originally Posted by Bianchigirll
Interesting. I presume you’ve heard of the International Roughness Index pertaining to roadways?
WE make them do that. Sometimes they have to grind etc to remediate non passing sections.

https://wisconsindot.gov/rdwy/stndspec/ss-04-40.pdf
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Old 03-04-18, 08:15 AM
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I have not thought about the dynamics of the geometry to that level. Thanks for sharing!

Do you think it is pointless to compare different configurations with this unit? Tires and wheel configurations on the same bike might be interesting even with a somewhat controlled test as you did with thumping the wheel.

Could you describe the challenges with collecting/analyzing the data?

How about increasing the size of the mounting hole to fit the skewer?
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Old 03-04-18, 10:19 AM
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When Strava is not enough...

Neat experiment. Thanks for sharing.
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Old 03-04-18, 10:49 AM
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How solid is that mounting tab? I would think that would add significantly to the measured fork resonance.
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Old 03-04-18, 10:58 AM
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I hope this continues somehow and is published and peer-reviewed.
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Old 03-04-18, 11:03 AM
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Originally Posted by seypat
Very cool!

I would donate $20 to the fund to purchase a 2nd device so you could continue the tests for the forum. That would be worth it for the discussions it would generate.
I'm in too. And I second the worry voiced by @droppedandlost about the flexibility of the metal angle used to mount the sensor.
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Old 03-04-18, 11:21 AM
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some some quick thoughts & questions about the instrumentation:

how much noise is there? what is the rms or peak value of the G readings while at rest?
Has the scale factor been checked in a basic way? i.e. place the sensor on a level surface in all 6 orientations (with the sensor's X, Y, and Z axes placed so that they are oriented with, and then against, the gravity vector), and verified that the reading is 1G in the selected axis, while the other axes read 0 G.

The size of the bumps encountered when these measurement were made wasn't disclosed, but I'm wondering if it makes sense that the longitudinal acceleration was nearly as great as the vertical acceleration. Would that mean that the wheel had encountered a slope of roughly 45 degrees? Or would it be different because the net force was accelerating only about half the mass vertically, while the longitudinal acceleration acts on all of the mass??
Or does it get messier because of the mass & spring effects, requiring the use of differential equations?

I'm an electrical engineer, and try my best to avoid these sorts of mechanical discussions, but still find them interesting. Any chance that some standardized bumps could be fabricated and see how the results match expectations? It would also be an opportunity to check the consistency/repeatibility of the sensor, and to mount it on different locations on the bike as you make repeated passes over the standard bumps.

Regardless, it's always fun to make some measurements and see if they matched your expectations!


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Old 03-04-18, 11:39 AM
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Originally Posted by steelbikeguy
verifiy that the reading is 1G in the selected axis, while the other axes read 0 G.

Steve in Peoria
That brought out my pedantic side. The G it's measuring is dynamic so it would be 0s all round until it moves. Similar to pressure in diving - although atmospheric is 1 bar, your starting pressure for a dive is considered to be 0 at surface, 1 bar at 10m etc. I think .
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Old 03-04-18, 11:52 AM
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Originally Posted by MiloFrance
That brought out my pedantic side. The G it's measuring is dynamic so it would be 0s all round until it moves. Similar to pressure in diving - although atmospheric is 1 bar, your starting pressure for a dive is considered to be 0 at surface, 1 bar at 10m etc. I think .
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I've worked with accelerometers quite a bit at work, designing a pitch & roll sensor for earthmoving equipment. Rotating the sensor will cause it to indicate 1 G in each direction as it is moved through the different orientations.

There are a number of interesting applications articles about accelerometers from the manufacturers, such as those in the lower part of this web page from Analog Devices...
Accelerometers | Analog Devices


The graphs presented show the nominal 1G offset for the vertical axis, and I'd expect to see the same in the other axes as the sensor was rotated.


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