*My investigation into the “golden rule of tricycle design” (having 66% of the weight on the front axle and 33% on the rear) showed that this was more restrictive than necessary, and that following a set of three design guidelines would better and allow greater innovation. These are:*

- The centre of gravity should be mounted as close to the two-wheel axle as possible to maximise
*rollover stability*. - The height of the centre of gravity should be less than half the track measurement and less than the distance to the front axle.
- If the centre of gravity is in the front half of the vehicle, the vehicle will be stable at all speeds, otherwise further calculation is necessary to determine the speed limit of
*lateral stability*.

*(Download the full technical paper here.)*

The release of the Atomic Duck design lead to a discussion on the ‘BentRider Online forums about the ideal weight distribution of a tadpole trike.

Because I wasn’t aware that the dynamics of three wheeled vehicles were particularly different to four wheeled vehicles, I asked for more information—this is one of the reasons open source works well, exchanging ideas to improve understanding. The responses suggested a requirement for weight distribution that was very prescriptive. To paraphrase:

The golden rule of trike design:

To ensure stability of a trike with two wheels on the front axle, the centre of gravity (centre of mass) must be a third of the wheelbase back from the front axle. This gives a static vertical wheel load of a third of the weight on each wheel; equal to 66% on the front axle and 33% on the rear.

What also came through was, that there wasn’t one clear reason why this rule existed. Suggestions were made about balancing rollover stability with braking performance, but my first article on tricycle stability and its research didn’t show anything so singular.

After asking about the source of the golden rule, purplepeopledesign told me about “Three Wheeled Vehicle Dynamics” from Jeffrey C Huston, Brian J Graves and David B Johnson from 1982. It seems likely that this is the original source for the rule, they don’t cite any previous paper in their references, it was originally published in 1982 and has been used as a source in an IHPVA journal article.

Specifically, they conclude:

To ensure lateral stability for the situation of constant speed straight line motion, it is recommended that the three wheeled vehicle with two wheels on the front axle be designed so that its mass center is located in the front third of the vehicle…

Huston, Graves and Johnson’s work on rollover stability is similar to what I presented in the previous post about tricycle stability, though they continued further. But I did find some confusion in the lateral stability calculations. When I re-ran their calculations, I came up with a different conclusion.

As a result, I propose that the golden rule might be better replaced by three design guidelines:

- The centre of gravity should be mounted as close to the two-wheel axle as possible to maximise
rollover stability.- The height of the centre of gravity should be less than half the track measurement (and less than the distance to the front axle).
- If the centre of gravity is in the front half of the vehicle, the vehicle will be stable at all speeds, otherwise further calculation is necessary to determine the speed limit of
lateral stability.

Unfortunately, the paper is not freely available online…which restricts how easy it is to discuss the contents. So I’ve reviewed the main findings about rollover and lateral stability, and how my results differ from the original authors this technical article: On the Golden Rule of Trike Design

This attached article is released under a Creative Commons Attribution-NonCommercial 3.0 Unported License. This licence gives you additional rights to share, copy, distribute, transmit, remix and adapt that work; if you do so for non-commercial purposes.

## 11 Comments

the drawing looks like most of the weight is to the rear ?

“it is recommended that the three wheeled vehicle with two wheels on the front axle be designed so that its mass center is located in the front third of the vehicle…

~~“it is recommended that the three wheeled vehicle with two wheels on the front axle be designed so that its mass center is located in the front third of the vehicle…”~~“If the centre of gravity is in the front half of the vehicle, the vehicle will be stable at all speeds, otherwise further calculation is necessary to determine the speed limit of lateral stability.”

“The height of the centre of gravity should be less than half the track measurement and less than the distance to the front axle.”

so a 16 ” seat height with battery pack underneath, lowers cog to maybe 12″… 40″ front track … or move battery pack more forward

or maybe in front of front axle like ….

http://www.evalbum.com/2311

Its not possible to recommend component placement without knowing every other item and their intended location, because every part affects position of the centre of gravity—including the rider.

It might be helpful to position the major components on a drawing of a side view of your vehicle. Then it’s a case of getting them to balance around a point at, or in front of, the middle of the wheelbase.

I’ll have forums and a wiki open soon that would be better places for individual design assistance, but you should also find some good community help now at places like BROL, recumbents.com and the trike doctor forums.

OK the relationship as I learned it was the trike will be stable of the resulting vector from all forces acting through the center of gravity stays within the boundaries of the triangle drawn between the contact points of the tires. so the CG has to be far enough to the rear that maximum braking forces don’t cause a stoppy (brake induced front wheelstand) and low enough that the rollover moment is less than 1/2 the effective tread width at the CG, with effective tread width being the ratio of the tread width to the portion of the wheelbase to the rear of the CG over the whole wheelbase.

You can put the CG as far to the rear as you want so long as the tread width is wide enough to keep it from rolling over in a turn.

I’d agree completely with your first paragraph, and the calculations I did in the post about tricycle stability come to equivalent conclusions to you for rollover stability. I’d argue if the CofG height is just “less than half the track and as close to the two-wheel axle as possible”, the rollover stabiltiy will be almost as good, without having to calculate exactly.

I recommended that keeping the height of the CofG “less than the distance to the front axle” would prevent any stoppies, assuming an absolute maximum of 1g deceleration in any condition.

Having the CofG in the front half of the wheelbase stops any speed related instability. For a Tadpole trike, this is unlikely to cause too many problems, with 30/70 weight distribution, the critical speed will be somewhere around 90mph. No real chance of reaching that in a velo! So the rollover stability will become a problem before the critical speed gets low enough to cause a problem.

However, for a delta, where the rollover stability gets better as you move the CofG back, it is worth checking that, fully loaded, will bags, etc. the critical speed stays out of the possible speed range, otherwise, the rear might start weaving about by it’s self!

If the CofG is in the front half, that problem doesn’t ever exist.

Dear Patrick, I am working on modelling the stability of tricycle. Pls how do I access d journals on this issue up to date from 1982.

Best Regards.

George

The link to “Three Wheeled Vehicle Dynamics” will take you to the page on the SAE’s (Society of Automotive Engineers) site where you can buy access to the paper. However, depending on your application, you might not need this specific paper. The authors used the “single track model” for tricycles and this is a well known simplification for modelling vehicle dynamics.

Paper is at: papers.sae.org/820139

Do you know of a simple computer modeling tool for CG calculation for a reverse trike?

I am reverse engineering a motorcycle based reverse trike and am fighting with the weight distributions.

I use LibreOffice Calc at the minute — a spreadsheet should be enough. Looking from a side view, if you know the weight of each part and the distance from the centre of the front axle, then you can calculate the position of the average by taking moments about the front axle (or any other zero position, centre of the front axle is traditional). You can also get axle loadings from this too — total moments (force × perpendicular distance) about any point must sum to zero, and the sum of all vertical forces must sum to zero.

If you’re reverse engineering a complete vehicle to find the centre of gravity, then you can find the static wheel loadings by putting a set of scales under each wheel (sum the values for the two wheel axle) to calculate the horizontal position of the average total load.