This is a continuation of a very interesting exchange I had with a member of this forum, @CCjon, also known as Jan, about the effort involved in riding a motorcycle with a sidecar, or: a rig.
Since I feel this particular topic is of general interest for all who want to know more about the technical aspects, I decided to dedicate a seperate thread to it.
First of all I think we should all briefly pause and pay tribute to Sir Isaac Newton, who left us some very valuable insight into the laws of motion that are applicable in this case. The first of which states:
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
As you can all attest, a well adjusted rig doesn't all by itself turn into a curve, unless the rider "impresses" a force on it, by some interaction with the handlebar, which is what he perceives as physical effort.
This effort can be computed, predicted, and thus compared between different rigs. One can then also derive suitable measures, if one want to lower the amount of physical effort required in piloting a rig around a curve.
A top-down view on the correlations goes like this:
-
A body going around a curve at a given speed experiences a certain centrifugal acceleration.
-
This acceleration times the total mass of the body results in a centrifugal force, which btw. is what Isaac Newton's 2nd law of motion states.
-
The centrifugal force must be balanced by the sideways friction of the tires, if the rig is to stay on its track.
-
The front wheel's share of this burden acts on the "effective trail" (I'll come to that further down) and creates a torque around the axis of steering.
-
The rider must apply a countering torque to the handlebar to maintain that radius of curvature.
These are the details of the individual stages:
-
The centrifugal acceleration can be easily computed as the product of velocity (squared) divided by the radius of curvature.
-
The centrifugal force is the product of the centrifugal acceleration times the total mass.
-
The load-sharing between the possibly three wheels is not quite as obvious. A little sketch may help in getting some insight:
Looking at the front and rear wheel alone, it's easy to identify the center of rotation of the tug. Both wheels follow nicely along a path tangent to their respective circles around the center of rotation. The side wheel however does not follow on a path tangent to the same center of rotation. At least some "scrubbing" will occur, and Toe-In makes this even worse. It's not clear whether the side wheel will support at all in picking up some share of the centrifugal force, and if so, how much.
What we do know however, is, that at the tipping limit the wheel load of the side wheel is by definition zero, so its sideways traction is zero as well. It will neither help nor hurt at that point. So at the tipping limit, the centrifugal force will have to be balanced by the front and rear wheel alone. The exact ratio can be determined with the help of the Interactive 3D Sidecar Simulator, and will probably vary slightly among different rigs. It's probably safe to assume, that the rear wheel bears around two thirds of the centrifugal force, and the front wheel around one third. Let's hold that thought for a minute - I'll put everything back into one coherent picture further down.
-
The "effective trail", which is the lever by which the front wheel's share of the centrifugal force produces the torque around the steering axle, can be derived from the following two sketches, which are to scale for my 2018 Ural cT. Units are millimeters and degrees:
Note, that neither the trail itself, nor the "effective trail" (blue line) are physically visible on a bike, no matter how hard you'll look at it. This is a theoretical concept which is accessible via drawing or computation only.
OK, now for some real-life
Example 1:
- A Ural cT, including rider "A", has a total weight of ~425 kg (~940 lbs.)
- The Interactive 3D Sidecar Simulator indicates, it has a tipping limit in right turns of 0.4 g.
- This results in a centrifugal force of 425 kg * 0.4 * 9.81m/s2 = 1668 Newton.
- The front wheel's share of this is 1668 Newton / 3 = 556 Newton.
- The torque around the steering axis at the tipping point is 556 Newton * 0.1243 m = 69 Nm (~51 lbf ft).
Example 2:
- For a BMW/EZS rig, including rider "B", I have allocated a total weight of ~455 kg (~1010 lbs.), assuming all else being equal.
- By doing some detective work I concluded, it has a tipping limit in right turns of 0.7 g.
- This results in a centrifugal force of 455 kg * 0.7 * 9.81m/s2 = 3125 Newton.
- The front wheel's share of this is 3125 Newton / 3 = 1040 Newton.
- The torque around the steering axis at the tipping point (again assuming all else being equal) is 1040 Newton * 0.1243 m = 129 Nm (~95 lbf ft).
Rider "B", by his own account, has a rig which is very planted and stable in right turns up to (and above) the legal speed limit. It's reasonable to assume, that driver "B" exhausts the legal speed limit, without exceeding it, because his rig supports it. In return, rider "B" experiences almost twice the effort (torque) at the tipping limit as rider "A". This is a considerable difference, in my view.
We can discuss, if there is interest, what can be done to reduce the required effort for rider "B".
If there is no interest, I'll leave you alone with this kind of applied physics lectures. Promise. 😎
Chris,
I for one enjoy reading your technical posts on this subject and would like to read what your suggestions would be to reduce the required effort for rider “B”. I am assuming you selected rider “B” because it is almost twice the effort of rider “A”, and your suggestions will show to what degree the benefit will be to make the changes and reduce the effort.
When you have time, maybe you could provide your thoughts for some of the following questions that have been taxing my brain for many years.
1 – What is to say the physical effort isn’t going to be a burden for most everyone who attaches a sidecar to their motorcycle?
2 – Wouldn’t the burden of the physical effort needed to be applied, be determined by the age, strength, physical stature and health of each individual driver?
3 – Once the physical effort of a rig is calculated, can it be determined by calculation what the ideal effort should be for the driver of that rig, or is determined by trial and error of the mechanical modifications?
4 – If the ideal effort of a rig is found based on a turning calculation, will it be too easy and become “twitchy” while trying to go straight down the road?
5 – I have found over my 45 years of sidecar driving, it just isn’t making turns that cause me fatigue; there are so many other road, weather, motorcycle load conditions that require constant steering inputs just to keep the rig going straight down the road.
Sorry for all the questions, there are more floating around in my tiny brain, but I’ll save them for another time.
Regards,
Bruce.
Bruce,
thanks for your interest.
- If I understand your first question correctly, you seem to be expecting that every sidecar rider experiences some degree of physical effort. Which I think is true, although I only recently learned that in fact there are considerable variations between different rider-rig combinations.
- You are also quite correct in assuming, that which one rider doesn't find worth mentioning, another rider may find overly exhausting already. This is the individual perception of individual people involved. And yes, this individual perception is likely to be affected by one's physical shape in general. But I don't know you guys and which shape you're in. What I'll be talking about is the actual, measurable effort, in terms of how strong do you (or a robot, for that matter) would have to pull/push the ends of the handlebar, to go around curves on a given rig.
-
Once the physical effort of a rig is calculated, can it be determined by calculation what the ideal effort should be for the driver of that rig, or is determined by trial and error of the mechanical modifications?
I'm not going to recommend an "ideal" setup. All I can do is point out, what makes the effort go up, and what makes it go down. It's up to the reader to apply this until he/she arrives at an acceptable level of physical effort.
4. If the ideal effort of a rig is found based on a turning calculation, will it be too easy and become “twitchy” while trying to go straight down the road?
I'm going to propose several measures: some are "behavioral", some do involve modifications of the rig, mechanical or otherwise. Mechanical modifications can carry the risk of the rig becoming less stable - I'm going to point that out if it applies. Changes in the rider's behavior leave the rig unaltered, in all respects.
5. I have found over my 45 years of sidecar driving, it just isn’t making turns that cause me fatigue; there are so many other road, weather, motorcycle load conditions that require constant steering inputs just to keep the rig going straight down the road.
This is probably the most difficult one for me to answer. It certainly helps, to have a well adjusted rig, in terms of toe-in, lean-out and alignment of front and rear wheel. A well adjusted rig should go straight at around 30 mph, hands-free, i.e without manual intervention. Bad weather, like rain, headwind, crosswind or worse cannot be compensated. I would avoid riding under such conditions, if possible. Bad road conditions are a matter of choice, too. And load conditions, other than the sheer weight? Please elaborate what you mean by that.
That said, here goes:
As I sketched in my previous post, the actual, measurable physical effort can be computed as the product of something like eight factors, and one division. If we could succeed in reducing each of these eight factors to 90% of their original values, we would have reduced the original effort down to 0.9^^8 = 0.43 , or 43% of what we started out with. Let's see, if we can do that.
I'll take the torque, which needs to be applied at the handlebar in order to go around a curve as the measure of the physical effort.
The torque "T" computes as:
T = ((mass of rig + mass of rider) * speed^^2 * (load share of front wheel) * (effective trail)) / (radius of curvature)
with:
- mass of rig [kg]
- mass of rider [kg]
- speed [m/s]
- radius of curvature [m]
- load share of front wheel [%]
- effective trail [m]
- Mass of rig: you can replace steel parts by parts made from light alloy or carbon, chop things off which are not necessary, empty the trunk from things which are not immediately required, like ballast. But frankly, shedding 10% off of the initial weight is either expensive, nearly impossible to do, or you may not like the looks of a stripped-down rig. You may as well trade your heavy rig for a lighter one.
- Mass of rider: keeping your own weight constant requires discipline. At least for me it does. Reducing your weight by 10% would require a tremendous amount of discipline, and only goes so far. So that's not very promising either.
- The speed at which you're riding. Now this you have under your complete control. And the speed enters the equation squared! Reducing the speed to 90% brings down the Torque at the handlebar to 0.9 * 09 = 81% already! And it reduces the wind pressure on your upper body, too. In case you don't have a fairing which does that already.
- Radius of curvature: narrow curves take a lot of effort. Wide curves are much easier to go around. Obviously you'll want to stay on the road, and not leave it because you'r overwhelmed by the necessary effort. But you have a choice of roads! Primary roads tend to have smoother tarmac, less, and wider curves. Selecting those would take a lot of effort out of riding. Depending on your inclination, this might also take some fun out of riding a rig. But you still can pick an advantageous "line" on secondary roads, by starting a curve on the outer edge, pulling into the inner edge (of your lane, of course), then towards the end of the curve go to the outer edge again. This artificially increases the radius of the curve, also lowering the effort.
- Load share of front wheel: you can influence this by adjusting your riding position. Sit back, lean back, straighten your arms, move your feet back to right underneath your seat will shift a greater share of your weight to the rear wheel, making the front wheel load become lighter, thus reducing the required torque. Beware though, that lightening the front wheel will increase the rigs tendency to "understeer", i.e. slide out of the curve. Try this gradually, and with caution only!
- Reduce the "effective trail": see the two sketches in my previous post. The effective trail hinges on several factors of influence:
- reducing the front wheel diameter will reduce the effective trail.
- changing a telescopic front fork to a leading-link type may reduce the effective trail. If you already have a leading link type front suspension, changing the link itself may reduce the effective trail.
- there are custom "triple trees". Some make the angle of the steering head steeper, others increase the "offset" of the fork legs from the steering axis, again reducing the effective trail.
Whichever way of reducing the "effective trail" you may be considering to go: these are very serious modifications which require an experienced dealership/rig constructor. And all of these will make the rig more "twitchy". Which may - up to a point - be compensated by application of a steering damper.
Hope this helps a bit.
Thank you for your input Chris.
Yes, thanks Chris. Great information!
I have been a hack driver for fifteen years or so. It has been my experience that if you find driving your rig requires too much physical effort, either your rig has not been set up correctly, or you have not modified your front end geometry to reduce trail sufficiently. I can drive my rig, hands off at any speed. The effort required to ride aggressively in the twisties is why I drive a rig. The fun in driving a rig is in coaxing it to go fast around corners. There is no fun in solo bikes. You just point them where you want them to go, and they go there. The bikes are so much better than you, and the lawyers controlling the results of your inputs are so paranoid you will do something stupid, that they ignore you when you do something stupid. If I want my rig to go around a corner quickly, the rig NEEDS to be convinced that it can do it. THAT is the fun of driving a rig. Solos are for sissies. When I am too old and feeble to handle my sidecar, I'll get a sportbike.
Thanks you Chris for putting this out here. I find this very interesting. I'm wondering if you want to comment on rider input to the sidecar rig while going through turns and how it affects the dynamics. I took the only three wheeled rider course offered in Minnesota shortly after I started riding three wheels. The instructor impressed upon us how moving just the upper body could help in negotiating corners. He used "clock positions" to get the idea across. On right hand turns I think he called it a three o'clock position where you move your upper body to the right and slightly forward. On left hand turns it would be called a 7 or 8 o'clock position where you lean your upper body to the left and slightly back. A practice exercise for this was a slalom course of cones set up in a parking lot. The more "body english" that you applied, the faster you were able to run the course (to a degree).
@hdgypsyman: I find your description of the physical action with your upper body quite "entertaining". And yes, I do believe that this may have an effect. But I can't see any physics reason which might contribute to a greater ease, with which you can go around curves, compared to just sitting "neutrally", so to speak.
I rather assume, that concentrating on moving your upper body like you describe, puts your mind(!) in the proper state to successfully do your first initial turns on a sidecar bike. Which is definitely a value in itself - no doubt about that.
And if we want to be really precise: moving your upper body towards the center of a curve, and doing so before entering that curve as such, will contribute a minuscule amount towards pushing the tipping limit outwards, towards a higher speed level. And by "miniscule" I mean: something in the order of a fraction of a single percent.
You can, btw., play around with different assumptions, also regarding rider position, in my Interactive 3D Sidecar Simulator.
https://vielzutun.ch/wordpress/?p=4730
