The adventure of the bicycle crash

The Show
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Spoiler alert: Read no further if you don’t want to engage in puzzler hints.

I’ve been stumped all week about the crashed bicylist. What was the cause? At first I was thinking it had to do with which side of the road you drive on in England, but I’ve since discounted that idea as pure bogosity. That was after I listened to the podcast a second time. My current thinking is that it has to do with the bicylist’s posture and the law of inertia. Anybody coming up with their own ideas on this one? Why did I change my mind? Well, there’s one other hint. When Ray read this question on the air, he added an extra word not appearing in the written puzzler.

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Yes, it does have to do on which side of the road.

If the convention of walking against traffic holds in England as it does in the US: The gardner would see Sir Richard ride off into void to the garner’s Right. However, the gardner is infact following Sir Richard in the left lane, and forces Sir Richard off the road to the Left of both the gardner and Sir Richard.

The second point is why wait to say something? If the gardner was innocent, he would know immediately that he was the sole witness and had nothing to fear. However, since he is guilty, he waited to insure that he was the sole witness, and thus waited.

RAY: I'd like to give you this Puzzler in the style of Sir Arthur Conan Doyle.

There had been a terrible accident in a suburb north of London, and Inspector LeStrade had been sent to investigate. Sir Richard Ashcroft was dead, and everyone agreed that it was an accident–although some suspected it was a suicide.

Sir Richard had been found on a rocky slope, his head dashed against one of the boulders and his mangled bicycle at his side. The facts seemed to speak for themselves.

He had lost control of his bike and had crashed. There had been no eyewitnesses, but finally an eyewitness emerged: Nigel–Sir Richard’s trusted gardener of many years.

Haltingly, he told his story: “I was walking back from town up that long hill leading to Sir Richard’s estate when I saw him riding toward me, sitting straight up in his seat the way he always rode. He was traveling at a high rate of speed. Suddenly, he jerked the handlebars to the left, and off the road he flew to his death.”

Later that day, LeStrade is discussing the points of the case with his buddy, Sherlock Holmes, over cognac and a few Arturo Fuentes cigars. Holmes says, "Bring the gardener in for questioning. He’s the perpetrator.

How DID Holmes know?"

Me, as a rider, I would tend to ride down a hill nearer the centerline, away from the loose gravel of the lower edge and towards the higher side of the hill. If I was riding uphill, I would still do the same. Gravity is a tememdous force and I would be careful in using gravity or minimize its influence on my control of the bike.

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Ok, I see what you are saying I think. When the gardener says the cyclist jerked the handlebars to the “left”, he meant his (the gardener’s) left, which would be the cyclist’s right. Since the cyclist would be on the left side of the road, he’s have to cross the entire road before going off the edge. So, in order that the cyclist go immediately off the road, when the gardener says I saw him jerk the handlebars “to the left”, the gardener must have been following the cyclist, not facing him. Do I understand you correctly?

Makes sense. But I still don’t see how the gardener (on foot) could be following the cyclist. Wouldn’t the cyclist be going too fast for someone on foot to keep up? Or was that part of the gardener’s ruse, and in fact the cyclist was just moseying down the hill?

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@GeorgeSanJose

"the gardener must have been following the cyclist, not facing him. Do I understand you correctly?"

No, that’s incorrect.

Nigel was “walking back from town up that long hill leading toward Sir Richards…” Remember that “Sir Richard was riding downhill at a high rate of speed.” So Nigel was approaching Sir Richard, not following him.

I had the right answer, mainly that jerking the handlebars to the left would make the bike veer to the right. Ray says that Sir Richard jerked the handlebars to the left, and the bike went off the road to the left. The detective knew that these two points did not match up with the reality of steering a bicycle.

I don’t think I buy the center of gravity explanation so much, but I can’t seriously defend that POV. I think it’s more about the geometry of leaning the bike so that the point of contact between tires and road is thus off center…but I can’t explain it any better than that, and I’m not convinced it’s right anyway. But long ago someone explained it to me and I was surprised to realize that indeed, when I want to turn left on a bike (I ride a lot), that I do indeed push/pull the bar so wheel goes slightly to the right. With that, the the bike leans to the left and turns left. Try it. This I think is the hardest thing for a small child to grasp when learning to ride a bicycle. I know it was for me.

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When you say “I had the right answer, jerking would make the bike veer right”, I don’t see that post in this thread. Did you post that comment elsewhere you mean? Or do you mean that’s what you were thinking when you heard it?

I think there’s two effects, both of which cause the bike to tip over to the right. The most important is simply the inertial force, the mass of the bike and rider moving a high speed/. This force is pointing straight ahead, downhill. When the front wheel is suddenly turned and pointed left, the bicycle and the rider’s inertial force still points straight ahead, which – since the front tire is pointing left now – will cause the bike to tip over to the right. If you draw a little diagram of his situation from above, and from the horizontal, and the direction of the intertial force located at the ctr of mass, it’s obvious the bike will tip over to the right. And the higher the center of gravity, the bigger the effect.

The second effect I expect is smaller, but it is the rotational inertia of the front wheel. If a rotating front wheel is forced to the left, there’s a corresponding force on the rest of the bike (and rider) turning the bike and rider in the other direction, to the right. That would also cause the bike to tip and fall to the right.

hmmm … When I turn my bike to the left, I first turn the front wheel to the left to initiate the turn, which then (as described a above) causes the bike to start to tip right, so I instinctively lean to the left to counterbalance it. The rider naturally then leans into the turn, to the left, when turning left. Otherwise he’d tip over to the right and bang his noggin on the pavement.

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@GeorgeSanJose

When you say "I had the right answer, jerking would make the bike veer right", I don't see that post in this thread. Did you post that comment elsewhere you mean?

What I meant by that was that I knew the answer when I first heard Ray give the puzzler, and I submitted that, but didn’t win (don’t know if they are picking new winners, probably not but whatever…).

So no, I hadn’t posted it anyplace on the website.

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I don’t think left or right really matters.
The gardner didn;t come forward when he saw the incident and infact waited before revealing supposedly, what he saw. The gardner only had to keep the knowledge to himself and be free.

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@Western
I am trying to equip my bike for a roadtrip. Slept outside in the rain and cold lastnight and discovered that I needed a sleeping bag liner and a better sleeping pad. The 7x7x4 dome tent kept the wind and rain out, but it really sweated.

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Do Anything in the PNW?

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"Ray says that Sir Richard jerked the handlebars to the left, and the bike went off the road to the left"
Where does it say which direction the bike went?
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I kind of have to disagree with the answer slightly. If Sir Richard was bolt upright and jerked the handlebars to the left, the bike would go left, or straight, but poor Sir Richard would be thrown to the right.

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I would think that mighty momentum would carry him straight forward. This has actually happened to me. I was going pretty fast and turned the handlebars quickly to try and avoid an obstacle. I had no time to lean into the turn. It was just a reflex action. I went right over the handlebars and did a face plant on the pavement. More disgusting road rash I hope you have never seen.

For him to fly off to the right, perpendicular to the vector of his travel, there would have to be a considerable force. And thus, this is why the gardener should be under suspicion.

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@gebobs
When I came up with my hunch about the answer they were looking for, I went back and listened carefully to Ray read the puzzler. The first time, he says only that Richard jerked the bar to the left, and went flying off the road, without specifying the direction. He then continued with the story, and later specified that Richard jerked the bar to the left, and then went off the road to the left. I think this approach downplaying the direction was his way of obfuscating. If you listen carefully, you’ll hear this slight difference in how he described it.

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@keith

I kind of have to disagree with the answer slightly. If Sir Richard was bolt upright and jerked the handlebars to the left, the bike would go left, or straight, but poor Sir Richard would be thrown to the right.

Yeah, I can see that, but I don’t think it’s right given that Sir Richard was going fast. At that speed, when jerking the bar to the left, the gyro effect of the wheels will create a lean to the right. I don’t think there’s much chance of resisting that at speed. That then will result in a right turn.

I’ll grant you though that if a bicyclist riding fast were to deliberately jerk the bar much too hard to the left than a good rider would ever attempt, momentum would probably toss him off expeditiously, mostly straight ahead, not off the road as the puzzler describes Nigel’s description. Maybe that’s what you are thinking?

So maybe their answer is quasi-bogus??

A good rider at low speed can make the bike do what you say, ie, go left when turning the wheel the left (I just tried that). This is what it takes to make a very slow speed turn, such as trying to ride a figure eight. It seems that at low speed, lean is more important than what happens to the handlebar. That explains riding no hands and making turns (I was pretty good at that when I was 12). I just think that at high speed, you can’t do what you say, and it’s after dark now so I’m not going to go out and confirm what I suspect is true. But steering the bar to the left will cause an instant lean to the right, and that results in turning right.

My point of contention with their answer is that I think there’s more physics involved than they explain, but since I’m not exactly sure how it works, I’m can’t really stand firm on that. But I think it’s related to the arc that the tire cuts when it is not vertical. But I’m on thin ice there!

I do think there’s some effect of the rider being familiar with the dynamics of a bicycle. I know that if I’m riding fast and need to turn a bit, my whole body just naturally knows what to do, I don’t really think about it. I lean a bit while I’m nudging the handlebar, it’s not one action causing the other. But I NUDGE the bar, I don’t jerk it at speed.

Maybe the physics is harder to see on a bicycle just because the rider is heavier than the bike and rider weight can overcome some of the gyro effect. But on a motorcycle, I think it’s really clear and obvious that pulling the left handlebar and pushing the right initiates a RIGHT turn. It takes only a very subtle touch at slow speeds to make the motorcycle lean and turn.

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Though they mention the gyroscopic effect, I’m skeptical that it would have any significant effect in the dynamics of this situation. And I have to admit, though I have an engineering degree from Rensselaer, the course in Dynamics is what convinced me to switch from mechanical engineering to materials engineering.

That being said, let’s consider some numbers. A “high rate of speed” is perhaps 7 m/sec for an old gent and let’s say Sir Richard has a mass of 70 kg. That gives him a momentum vector in the direction of his travel of 500 kg-m/sec (maintaining one sig fig).

Irrespective of this forward motion, a force would need to be applied to accelerate the good sir’s body from zero in the direction perpendicular to the forward motion. That force would need to be sufficient such that he would not be able to recover and force him over the edge some few to several meters distant. For the heck of it, let’s say it would require an acceleration of about 10 m/s to push him over the edge. Thus the force would be about 700 newtons (or about 160 pounds…sig figs be damned).

That’s as far as my dynamics will take me and someone more versed in the topic may plainly see why I switched majors. So hazarding an argument from personal incredulity, I don’t see the gyroscopic effect having anything like that kind of stabilizing force. I believe it is a minor factor in the stability of a bicycle and results only in small corrections and forces. Just guessing, under a few newtons.

So the answer is technically correct though not for the reason the answer seems to state. I don’t think Nigel could have seen what he described with only what we know. If Sir Richard had suddenly jerked the front wheel, whichever direction, his momentum would have carried him directly forward. Other minor forces - the gyroscopic force, the force between the tire and the pavement, the force between his arms and the handlebars, etc., etc. - might result in some small lateral motion but probably not enough to throw him over unless he was riding a foot or so from the edge and just toppled over.

Some other force must have been at play, but it’s speculative at best to think that it was the gardener that did it. But so much for over thinking (and addled over thinking it probably is). Good times.

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@gebobs
My uninformed sense of this vaguely agrees with you, not that I remember nearly enough physics to follow your calculations ;=).

I think the point is that if Nigel’s story had been truthful, the bike would have turned right, not left, causing the Sir Dickie to ride off the road and then crash. You seem to be working on explaining how the old boy got flung off the bike.

But we probably are overthinking this. I just think that Ray’s concept was tricking people with the reality that the bike would turn right if the bar was jerked to the left. By describing the accident twice but only once mentioning the direction, it was kind of “sleight of hand” deception to throw people off the route of the intended answer.

But then it all would come down to just how hard Sir Richard jerked the bar, and whether that was enough to throw him off right away or to make him turn. I’ll guess that Ray’s unspoken intention is that the bike turned, not that it flung him off.

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"I think the point is that if Nigel's story had been truthful, the bike would have turned right, not left, causing the Sir Dickie to ride off the road and then crash. You seem to be working on explaining how the old boy got flung off the bike."

I don’t suppose it matters if he gets flung or not. He and the bike both carry momentum proportional to their mass. They will both continue forward and will only move laterally with applied force. In my opinion, gyroscopic forces cannot account for any significant lateral movement. They are very small. Even as regards a nearly balanced bike, they only provide small corrective force. Their effect will be negligible when a bike is jerked one way or the other.

So although I think the explanation is wrong (or quasi-bogus as you say), it leads to the same result. Some other force must have been applied. But the gardener has nothing to worry about unless he does something stupid like when he came forward with his recollection (truthful or not). It could have been a stiff breeze, a pothole, or the spectral hand of Sir Richard’s late wife who he poisoned after she found him buggering Nigel. :wink:

The gyroscopic explanation reminds me of the Coriolis effect. People hear about it and misconstrue the physics. People will say that toilets flush and tubs drain in opposite directions in the northern and southern hemispheres due to the Coriolis effect. Of course, that’s a myth. The forces that make hurricanes rotate clockwise in the Caribbean make them rotate the opposite way south of the equator. And on the equator, hurricanes are generally absent which makes Aruba a safe destination, weather-wise anyway. On the scale of a toilet though, the forces are infinitesimal.

"I'll guess that Ray's unspoken intention is that the bike turned, not that it flung him off."
Yeah, I think that's right. I like the puzzler. It made me dust of a layer of cobwebs. Many to go.

Sometimes in cases like this, only real empirical evidence will do. Now where’s that bicycle pump?

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I can’t even begin to explain this, but I think the force you are describing turns into a g-force as the bike veers, there’s a side force where the tire meets the road. I think that’s where your momentum goes. The sharper the turn, the more g-force. Riding straight, you don’t feel it, but make a turn and that change of direction puts a force into the road. Or something like that.

Get on a bicycle and feel it yourself: go fast, then make a sharp turn into a side street. You’ll get pushed into the seat, pedals, hand grips, more than you did going straight.

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Right. Other forces. Tire on road. Hands on handlebars. This is a result of inertia…resistance to any change in the velocity/momentum vector, a change in either direction or magnitude.

"Get on a bicycle and feel it yourself: go fast, then make a sharp turn into a side street. You'll get pushed into the seat, pedals, hand grips, more than you did going straight."
Concur though this is not due to gyroscopic forces.
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As I said at first, I can’t explain this, though others surely can. My point is that there is an increase in force on the rider when turning at high speed, that is the result of the momentum being converted to accelerating in a different direction. The friction on the tires keeps the bike from falling as the bike leans, and of course, lean too far and the force of momentum exceeds the friction component…resulting in road rash.

How about that for fabricating a lame and flimsy description? ;~)
No more, I promise!!