Dual Radii

Crownring gets its efficiency from the profile and timing of its dual radii. Crownring works in conjunction with pedal stem leverage and bio-mechanical posture. By aligning the crown with the stronger straight leg and the near peak leverage, Crownring brings your three best power advantages together at an optimal time. Timing is crucial for peak efficiency.

Timing

Timing referrers to the peak crown execution relative to the pedal position. On an upright bicycle, peak is when the crown points straight upward, where its reach pulls the hardest on the chain. Timing would mean changing the pedal position relative to crown peak. If you change timing it changes performance. Delayed timing pedals easier than advanced timing. You can learn more about crown timing from the Timing link on the left panel.


Leverage

To understand the efficiency of Crownring you need to know the efficiency of the standard chainring. While a pro bicyclist will get more efficiency from a stroke with a practiced tangential application of force, the most of us just push the pedal. We rely on a linear application of force. The pedal lever varies in mechanical advantage directly effecting torque. Torque (t) is the rotational force (r) generated by applied force (F) to the effective lever arm (eff). The math is this:

t = F x reff

All it means is the down push of the force is changed by the effectiveness of the rotating lever arm. Leverage is measured by the distance the force is applied from the crank axle. An adult bicycle commonly has a 7 inch pedal arm (resulting in a 14 inch stroke). Throughout the stroke, leverage ranges from zero at Top Dead Center (TDC) to 7 inches at its mid stroke maximum.

Here is the important part. You cannot physically use the entire stroke to generate power. Lets consider the first half of the stroke. From TDC up to about 1/4 stroke your force is not enough to overcome the resistance as you try to draw 4 and even 6 times the chain to the fraction of the stroke. This is referred to as the Dead Zone. At about 1/4 stroke you draw equal chain to the stroke advance. We are speaking of ratio. Here, where leverage is about half of its potential, your ratio is 1:1.

The problem comes as the rotation continues and the effective leverage gets longer. The ratio changes giving the rider a mechanical advantage of about 2:1. The 1/4 stroke position is about twice as hard to power as is the easier 1/2 stroke position because you draw twice the chain at 1/4 stroke as your do at 1/2 stroke.

A stroke on average is about 1/2 second. This means the time between hard and easy is only about 1/8 of a second, not enough time for your foot to double its speed before force can be applied. Technically it falls under "Rapid Force Development (RFD)," the duration at which a force can expand.

You cannot use the Dead Zone. It would take as much as 1000 pounds of force. The effective leverage is essential for you to power a bicycle, but it changes faster than your force can be applied. In this you only use about 1/3 of your stroke to generate power. You use the 1/4 stroke (and its ratio equivalent 3/4 stroke) for acceleration, or you use the 1/2 stroke (most powerful) for casual and uphill riding. But you cannot use them both within the same stroke. Your foot isn't fast enough. You ether push hard and go fast, or push easy and go slow, each phase using its most effective zone.

The slower you pedal the more time you have to transition and the more of the stroke you convert to power. The faster you go the more the effective leverage enters into the Dead Zone. The dynamics involved in a pedal stroke are far more complicated than "pushing down" and there is more to it than what I've described here, but if you understood these few paragraphs it should give you adequate comprehension to grasp why Crownring is so much more efficient than a standard round chainring.


Note: Crownring is not the only dual radii chainring. There is a non round chainring called the oval, or elliptical, designed to counter the changes in leverage. However, Crownring is the only non round chainring that provides dual ratios within the same stroke. It is these dual ratios that give a rider their best advantage.


Ratio

When you use a bicycle the chainring decides the chain draw that acts on the rear cog. Today a common chainring is 44T. T means teeth, so 44 teeth occupy its perimeter. Ratio is the relation between the chainring and the rear cog. Common is a 16T cog, often as a single speed freewheel. 44T/16T determines a ratio of 2.75:1. One revolution of the chainring rotates the wheel 2.75 times.

At the ratio of the example your strength is multiplied 2 and 3/4 times.  This multiplication is what makes the bicycle the most efficient machine ever invented.

The designation for a common chainring is its T value; 48T, 34T. The designation for a Crownring is (draw)T/low-high(crown size). The high is the dominant value. It determines the speed. The Draw is simply the tooth count.

When we look at these together, as in 40T/36-49(2) the high, 49, results in the same speed as a 49T chainring. Consider that this is accomplished with a chain draw of a 40T chainring. Also within that 40T draw is the radius of a 36T chainring. These values come into play under different conditions, but even as they are separate they work in unison.

Lets make an example of a 48T chainring. It has a 48T radius through both the first half and second half of the stroke. Throughout this stroke your leverage inches range from 0" at Top Dead Center (TDC) to about 7" at center stroke, and back to zero. The radius remains constant but the leverage changes alters the ratio.

48T at 1/2 inch links is 24 teeth per stroke, or 12 inches of chain pull. At about 43° of rotation the ratio is near to 1:1. If your foot falls one inch then you pull one inch of chain. The center of the stroke, at full leverage the ratio is about 2:1. If your foot falls one inch you pull only 1/2 inch of chain. At 135° the ratio is back to 1:1. After 135° the leverage shrinks rapidly, making the continued radius much harder to pedal.

Crownring peaks and then declines. Timing is relative, but to put it simply, the crown declines at the same general rate as the leverage and thus continues the same demand of force for the duration of the crown decline. It doesn't increase ratio at the end of the stroke as a chainring does. Crownring maintains it.


Bio-mechanics

Even more important than leverage is how your leg posture changes the force applied. Consider a deep knee bend (a squat). As you rise up from the low posture it becomes easier after you've reach halfway. Add a bit of weight to your shoulders and you'll notice it even more. The bent leg, or the knee up position on a bicycle, has less than 2/3 the force of the straight leg.

A Crownring takes advantage of this change in force. Timed with your strength increase, Crownring raises the radius, accelerating the bicycle and adding to kinetic energy. Kinetic energy is the stored energy from the combined weight of you and your bicycle which keeps you moving. Inertia is the property of motion that resists change. Inertia helps maintain the bicycle's speed while acceleration requires a force to change the object's velocity, thereby affecting its kinetic energy.

As you pedal along, the bicycle travels. If you stop pedaling it still travels. Resistance eats up kinetic energy and the bicycle slowly slows. To compensate you pedal. You only need to input force equal to the resistance. Even under acceleration your force is only equal to the resistance of that acceleration—which is a change in inertia. Pedaling overcomes resistance but kinetic energy is what moves your bicycle. The more kinetic energy you've stored the easier it is to pedal.

Crownring uses the increase in straight leg strength to convert the additional force into speed by way of increased radius, thereby generating kinetic energy which enhances subsequent strokes.

The great thing about Crownring is its rise in radius goes completely unnoticed. Unlike the common chainring, both first and second halves of your stroke work you about the same thus saving energy at the top and increasing kinetic energy at the bottom.

Real-World Power Evaluation: The Scale Test

To quantify the efficiency of the Crownring, we measured the raw force application available in different riding postures. Using a scale test, the results were clear:

• Seated Position: Generated 120 lbs of force.

• Standing Position: Generated 200 lbs of force.

By timing the Crown to engage during the standing phase (the straight-leg power stroke), a 54T/48-66(3) Crownring (The very first Crownring test) allows the rider to utilize the 66T high-radius peak. Because this peak aligns with the body's maximum 200 lb force capacity, the rider experiences no more perceived effort than that of the standard 48T round ring top of stroke.

The Efficiency Gap: By enabling a 66T output for the same effort as a 48T input, the Crownring provides a calculated 37.5% increase in efficiency.

Why the Math Works

The math of torque is t = F x reff. In a standard round ring, you are stuck with a constant radius even when your force fluctuates. You waste the 200 lbs of "standing power" on a radius accessible at 120 lbs.

Crownring solves this by expanding the radius only when your body is at its strongest. You aren't "working harder"; you are simply stopping the "waste" of your leg's natural strength.

Add Momentum

By increasing momentum the Crownring reduces the effort of the 48T radius following the 66T radius giving further reduction in overall effort. Because kinetic energy increases with the square of speed (v2v2), a bike at 20 mph has 400% more stored energy than at 10 mph. This momentum carries you through the dead spots so perfectly that your "interruption" in power is less than 1%. The high radius uses the biomechanical increase to provide 200% more stored energy (10 mph vs 20 mph). This gives a sense that the 48T radius of Crownring is half as hard as the 48T of a round chainring. We cannot keep that 50% reduction because the 66T of the high radius increases effort. But due to the biomechanical advantages the 66T has no more perceived effort than the 48T low radius of the same stroke. Your energy output is the same with a 54T/48-66(3) as it is with a 48T chainring while delivering 66T speed.


Crown

It is the crown that transfers the energy from your straight leg to the chain. Your strength increase peaks with the crown engaged with leverage at about 80% and the foot still with room to travel downward taking advantage of gravity. At this posture a standard chainring has all the benefits that Crownring can provide, given an equal radii. The example has been of a 40T(2) Crownring which has a high radius equal to 49T and compares closely to a 48T chainring. For this brief moment the Crownring and the chainring are nearly equal in energy.

It is after this point that Crownring improves the efficiency. The chianring continues to increase ratio as leverage decreases. It quickly exceeds the rider's capacity to input force. The Crownring keeps a constant ratio as leverage decreases by also decreasing its crown pitch, which prolongs the force input at a ratio much lower than what the chainring demands. Not only does the declining crown prolong applied force, but it results in a smooth and natural end of stroke.

During the first half stroke a standard chainring demands the same applied force that the second half stroke demands. With the bent knee being less than 3/4 its straight strength, a rider must push harder to cultivate enough power to move forward. In the least that is a 25% loss of energy as compared to the second half stroke.

Crownring reduces the radius during the first half stroke making less of a demand for application of force. The Crownring curtails the chainring's 25% loss of energy which reduces stress and prolongs stamina. By demanding less of the bent knee there is more energy available for the second half stroke.

Another crown advantage is the uphill climb. By maintaining the low radius through the greatest leverage the Crownring offers a more powerful climbing ability. But it goes a step further than just dropping the gear ratio. By cultivating the added strength of the straight leg, the recovered speed maintains kinetic energy.

When you fail on a hill it is because your speed has slowed and no longer provides kinetic energy to coast to where the pedal is again useful. Kinetic energy is the only reason your can ride a bike up a hill. Once lost it becomes impossible to reset your pedal for force input.

The Crownring's low radius through the first part of the stroke is much more likely to benefit the climb than would the constant radius of the chainring. But it is the low radius of the center stroke that benefits climb. Beyond that, converting straight leg strength to speed through the high radius it maintains kinetic energy which is essential for the climb.


Crown Size vs Effort

Take a common chainring size and compare it with the three practical crown sizes. 44T is the chain draw. On a round ring the variance percent is zero. To push the bike forward your low strength must work harder than your high strength. With Crownring the crown size makes the difference in efficiency.

• 44T Round                      0%
  
• 44T/42-46(1)             9.52%
• 44T/40-52(2)           26.09%
• 44T/38-56(3)           38.30%
  

Although the chain draw is equal across each of the four chainrings the energy output increases by its percentage. The size 3 crown is nearly 40% more efficient, just inside of the 40% of the Scale Test. As long as the percent does not exceed the strength increase the rider does not register the effort of the high radius. The 56T of the 3 crown is no harder to power than the low strength of the 44T round chainring, even though it delivers the speed of a 56T chainring.


Efficiency

To break all this down lets chop a single downstroke into quarters.

1. Crownring provides a more effective low ratio through the first quarter stroke conserving energy.
2. Crownring maintains a low radius through the second quarter stroke increasing climbing power.
3. Crownring delivers a high radius through the third quarter stroke where force is strongest increasing speed beyond its T-value.
4. Crownring declines the ratio through the forth quarter stroke resulting in prolonged input of effective force even as leverage is lost.
   

Every phase of the stroke is benefited by Crownrings unique dual ratio delivery. Crownring excels in every terrain. Compared to the conventional bicycle drive, when the chain draw is matched Crownring is easier and faster. When the low radius is matched Crownring is faster. When the high radius is matched Crownring is easier. A common chainring has no physics to compete with Crownring.

No matter how you slice it, Crownring is just better.