Flywheel & Kinetic Energy
Calculation & Interpretation
Background
Kinetic energy storage is essential for an elliptical machine to overcome its inherent low-torque zone and provide smooth, low-impact resistance.
Flywheel is the primary component that stores the kinetic energy and transfer it back to the drivetrain when needed to maintain movement continuity.
Low-Torque Zone
Elliptical machines have a
Flywheel & Kinetic Transfer
To overcome the low-torque zone, a flywheel is used in ellipticals to store rotational kinetic energy in the system and transfer that energy back to the drivetrain to help it pass through the low-torque zone.
In this article, kinetic energy refers to rotational kinetic energy.
The kinetic energy stored in the flywheel largely represents the kinetic energy stored in the entire machine drivetrain. It is determined by the size, shape, weight, and rotational speed of the flywheel.
Rotational Kinetic Energy Calculation
Rotational Kinetic Energy
The rotational kinetic energy of a flywheel is calculated as:
KErot = 1/2 Iω2
where:
| KErot | Rotational kinetic energy |
| I | Rotational inertia of the flywheel |
| ω | Angular velocity in radians per second |
Rotational Inertia
For an uniform solid cylinder type of flywheel, its rotational inertia (I) is calculated as:
I = 1/2 mr2
where:
| S | Flywheel Shape Factor |
| m | Flywheel Mass |
| r | Flywheel Radius |
Rim-weighted Flywheel
In reality, most elliptical machines utilize a rim-weighted flywheel. This type of flywheel has higher rotational inertia on the same mass, because the flywheel is designed to have the majority of mass concentrated near the outer rim.
A shape factor needs to be applied to the calculation:
I = S · (1/2 mr2)
Rotational Kinetic Energy Formular
Combining the above two equations:
KErot = 1/4 Smr2ω2
This formula shows why both flywheel size and flywheel velocity matter. Increasing the radius increases kinetic energy by the square of the radius. Increasing rotational speed also increases kinetic energy by the square of the angular velocity.
Rotational Kinetic Energy Calculation
In the rotational kinetic energy formula, the shape factor, flywheel mass, and flywheel radius are fixed properties of the flywheel.
Flywheel Shape Factor Estimate
The shape factor used in the calculation of this article is an engineering estimate based on a LB007 flywheel model.
LB007 utilizes a a spoke type, rim-weighted flywheel (weight 2.5 kg, 0.12 m radius) that can be simplified as below:
| Flywheel Section | Estimated Mass Share | Effective Radius | Estimated Rotational Inertia |
| Outer rim | 75% | 0.11 m | 0.02269 kg·m2 |
| Three spokes | 15% | 0.075 m | 0.00211 kg·m2 |
| Center hub | 10% | 0.03 m | 0.00023 kg·m2 |
Therefore, the rotational inertial of the LB007 flywheel is:
Irim-weighted ≈ 0.0250 kg·m2
For a solid cylinder flywheel of 2.5 kg and 0.12 m radius, the rotational inertia is:
Isolid cylinder = 1/2 mr2 = 1/2 × 2.5 × 0.122 = 0.0180 kg·m2
The shape factor compares the LB007 flywheel rotational inertia with a solid cylinder of the same mass and radius:
S = Irim-weighted / Isolid cylinder = 0.0250 / 0.0180 ≈ 1.39
S ≈ 1.4
This means the rim-weighted spoke-type flywheel is estimated to have about 40% more moment of inertia than a solid cylindrical flywheel of the same mass and diameter.
Angular Velocity Assumption
The angular velocity of the flywheel, however, is a variable determined by the pedal stroke rate and the transmission ratio.
To compare different elliptical designs, let's assume an average exerciser pedals at a rate of one pedal stroke per second.
The one pedal stroke per second rate provides a reasonable basis for estimating rotational kinetic energy.
This gives the crank rotation speed of 60RMP.
The 60RMP crank rotation speed also provides a consistent reference for comparing KErot between different elliptical models.
Calculation Comparison
This calculation is based on a pedal stroke rate of one pedal stroke per second and a flywheel shape factor of 1.4.
| Typical Commercial Elliptical | NordicTrack AirGlide 14i | LB007 Vertical Elliptical | |
| Flywheel Approach | Size Approach | Size Approach | Velocity Approach |
| Drivetrain | Direct-Drive Flywheel | Direct-Drive Flywheel | Two-Stage Transmission |
| Transmission Ratio | 1:1 | 1:1 | 1:15 |
| Flywheel Diameter | 18 in | Estimated 20 in | 9.4 in |
| Flywheel Mass | 25 lb | 32 lb | 5.5 lb |
| Flywheel Speed at 1 Stroke/sec | 60 RPM | 60 RPM | 900 RPM |
| Estimated KErot | 8 Joules | 13 Joules | 111 Joules |
These are simplified engineering estimates intended for comparison. Actual values may vary depending on detailed flywheel geometry and measured operating speed.
Why Kinetic Energy Matters
Low-impact exercise is often described as being gentle on the joints. In mechanical terms, this means the resistance should not change abruptly. Sudden force changes can create a jerky feel at the pedals and increase stress on the knees and other joints.
A flywheel helps reduce these abrupt changes. When sufficient kinetic energy is maintained in the rotating system, the motion does not stop or hesitate at the Zero-Torque Spot. The flywheel carries the drivetrain through the Low-Torque Zone and helps the resistance feel smoother.
Two Approaches to Flywheel Kinetic Energy
The rotational kinetic energy stored in a flywheel depends on two main factors: the flywheel's moment of inertia and its angular velocity.
There are two general approaches to increasing flywheel kinetic energy.
Size Approach
The traditional approach is to use a larger and heavier flywheel. A larger diameter places more mass farther from the center of rotation, increasing the flywheel's moment of inertia.
This is the common approach used in conventional ellipticals. Since many conventional ellipticals directly drive the flywheel from the crank, the flywheel rotates at the same speed as the pedal stroke rate. With low flywheel velocity, size and weight become the primary ways to increase kinetic energy.
Velocity Approach
The second approach is to increase flywheel rotational speed. Because kinetic energy increases with the square of angular velocity, increasing flywheel speed can be a very effective way to increase stored kinetic energy.
This approach requires a transmission between the crank and the flywheel. The transmission allows a smaller flywheel to rotate much faster than the pedal stroke rate.
Interpreting the Comparison
The conventional elliptical and AirGlide examples rely mainly on flywheel size and weight. Since their flywheels rotate at the pedal stroke rate, their kinetic energy is limited by practical flywheel diameter and mass.
The LB007 example uses a different method. Its two-stage transmission increases flywheel speed, allowing a smaller flywheel to store substantially more rotational kinetic energy.
This illustrates the difference between the size approach and the velocity approach. A large, slow flywheel can store kinetic energy through size and weight. A smaller, faster flywheel can store kinetic energy through rotational speed.
Summary
An elliptical machine needs a flywheel because the crank-driven motion contains Zero-Torque Spots and Low-Torque Zones. At these positions, the user's downward stepping force does not effectively rotate the crank or flywheel.
The flywheel stores kinetic energy during the stronger part of the stroke and transfers that energy back into the drivetrain as the crank passes through the Zero-Torque Spot and Low-Torque Zone. This kinetic energy transfer helps maintain movement continuity and smooth resistance.
Conventional ellipticals generally use the size approach, relying on larger and heavier flywheels because the flywheel rotates at low speed. The LB007 uses the velocity approach, using a two-stage transmission to rotate a smaller flywheel at higher speed.
From a physics perspective, the flywheel is not important simply because it is heavy. It is important because it stores kinetic energy and transfers that energy back into the drivetrain when the motion system needs it.