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## Matthias’ physics lesson: Understanding steering geometry

Matthias Reichmann, inventor and developer of the Virtual Pivot Headset explains the physical background of the steering geometry:

## Stability on the single track vehicle

Why doesn’t the bicycle or motorcycle tip over? Because someone is sitting on it and keeping the balance? Yes and no – because above a certain speed, single-track vehicles can just keep going themselves. But not perfectly straight, they “lurch”. And exactly this lurching is the mechanism that stabilizes this actually unstable system. But now we go back several steps – I try to keep the explanation short and understandable.

Our wheels have a so-called “mass moment of inertia”, which depends on the radius and mass. The gyroscopic forces result from the mass moment of inertia. We experience these when we take an wheel and let it rotate. If we tilt it counterclockwise from vertical, it will turn in to the left (and clockwise to the right). In other words, if we are riding a bicycle and we tilt to the left, our steering will turn in, we will make a turn. From the turn we get a centripetal acceleration at the center of gravity of the whole system, multiplied by the mass we get the centrifugal force, multiplied by the center of gravity height we get a moment. This moment restores our bicycle. According to Mr. Isaac Newton, however, we are an inert body that simply behaves inertly without the influence of a force from outside – in other words: it tilts to the other side. Here the game starts all over again, via the gyroscopic forces of the tilting front wheel, it steers in again, drives a curve and sets itself up again accordingly. Our unstable system thus stabilizes itself by permanently driving curves – it lurches.

How much it tilts, how large the curve radius is, and at what frequency it lurches depends on a variety of parameters:

• Mass moment of inertia of the wheels, depending on radius, mass distribution and mass
• Riding speed
• Center of gravity height of bike and rider
• Steering geometry – steering angle, offset and wheel size: These 3 parameters result in the trail or caster.

If we want to actively influence our stability, the easiest way is to vary the trail. Here we will now explicitly deal with the value of the offset. We shorten the trail via a longer offset. The trail is the lever arm of the reset torque of the front wheel. By shortening the trail (=longer offset), our steering becomes more reactive, more agile, and in extreme cases possibly even more nervous. However, this plus in agility makes the steering react faster to a tipping of the bike – the lurching is reduced, the bike stabilizes faster. In other words, the amplitude of the lurch decreases, the frequency of the lurch increases. This results in an apparent paradox: more agile/nervous steering leads to more stable behavior of the bike as a whole.

In the other direction, shortening the offset results in a lengthening of the trail, which leads to a “stiffer” and less reactive steering, causing the wheel to tip further before it sets up again.

There is no “better” or “worse” here. The bike’s behavior simply has to suit the rider.

In principle, however, we cherish the basic recommendation:

• Steep steering angle = short trail-> tendency to shorter fork offset to stabilize the steering
• Slack steering angle = long trail-> tendency towards longer fork offset to inject some agility into the steering.

An adjustment of the offset is quite noticeable for experienced riders. A modern DH bike has a trail of approx. 130 to 140 mm – a difference of 8 mm corresponds to about 6%. Incidentally, the same trail change also results from a 1° change in the steering angle – experienced riders definitely feel this. However, due to the diversity of the parameters of the overall system, it makes no sense here to calculate the perfect value in concrete terms – you have to “feel” it. And our VPH system is perfect for this – simply change the offset in a few minutes and try it out instead of buying a new fork.

If you want to dive deeper into this topic, I recommend the following link:

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## Suspension optimization #1 for the SENDuro

Many of the current shocks offer very a wide range of adjustments. In addition, special tunes can be ordered from many suspension manufacturers. To find the best possible setup for the SENDuro, we visited Stefan from insanityofgravity. Stefan is passionately dedicated to all topics related to mountain bike development, optimization and tuning. On his blog https://insanityofgravity.blogspot.com/, Stefan challenges prevailing opinions and tries to confirm certain theories through calculations and experiments. Also through his mountain bike projects, every ambitious tech nerd should have come into contact with Stefan in the media. His Ultra High Pivot Enduro has at least generated some interest: https://www.pinkbike.com/news/bike-check-insanityofgravitys-titanium-ultra-high-pivot-freeride-bike.html

To get reliable data, Stefan does not rely on the manufacturer’s data, but measures the spring and damping characteristics himself.

The self-designed test rig for the spring characteristic compresses the shock step by step and records the resulting force.

The measured values are transferred to a table and output as a curve. The spring curve can then be superimposed on the leverage ratio curve of the frame using special software. The result of this measurement confirmed our impressions from practice: The Fox X2 with its relatively high air chamber volume harmonizes very well with characteristic of the SENDuro frame.

In the second step, the damping characteristic is measured. Missing adapters are made by Stefan in his own workshop.

A dynamometer is required for recording the damping curve. The shock is compressed at different speeds and the resulting forces are measured and recorded. By compressing the shock at different speeds, a very precise distinction can be made between high- and low-speed rebound and compression.

Different settings of the compression and rebound damping can now be used to try to approximate an ideal damping characteristic. If the adjustment range of the shock does not allow this, special tuning of the shock can be considered. However, since personal preferences, the personal fitness level and the preferred trails also play a role in the selection of the damping curve in addition to the theoretical values, a great deal of intuition is required here.

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## SENDuro – What`s next?

We have been a bit quiet in the media lately and some of you might have wondered how things are going or what the current status is.

We have spent a lot of time on the SENDuro, have tried different setups, have ridden some races and had a really good time on the bike.

We are more than happy with the kinematics and the function of the frame and don’t want to make any more changes here.

As indicated in the last newsletter, we have revised the bearing seats on some parts and improved some details. Also, the rear end now come with an additional adjustment option, with which the geo can be fine-tuned. Thus the SENDuro probably is one of the best adjustable enduros on the market. To all the adjustment options still comes a separate video.

Unfortunately, we are behind our original schedule and will not make the first planned production in June. With the components that are welded to the frame, there were unfortunately material problems and we had to find a solution with our supplier here. However, the problem has now been identified and resolved and we can confidently move on to the next round.

At the moment we are waiting for new parts and will probably be able to release the final state of the frame at the end of May and then plan a production date. For all those who have already reserved a frame, this unfortunately means that some patience is still necessary.

As soon as we are ready, there will be an official launch and information about the pre-order. Everyone who has already reserved a frame will get priority access to the preorder.

Thanks for your patience and if you have any questions, you can always contact us by mail, phone or whatever. See you soon!

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## SENDuro // ride24

The South African news magazine ride24 published a small article about the Reichmann Engineering SENDuro based on the article from The European Bike Project.

“The Senduro could set new standards for rear-suspension performance.”

ride24