Physics in Elliptical Machines
When you byciclying, the forwarding momentum will help you pass through the the dead spot, so you have a smooth ride.
However, for a elliptical machine or a staionary bike, we will need to create a rotational momentum, or rotational kinetic energy to help pass the dead spots, avoid jerk or stutter caused by those dead zone, producing smooth and low-impact resistance.
Moentum and kinetic energy are two approaches to explain the physics of elliptial machine, while kinetic energy can better explain the relationship how the flywheel diameter, weight and rotation speed are related to the smooth, low-impact resistance of a elliptical machine.
Elliptical machines are all designed to have a flywheel. The role of the flywheel is to keep the movement fluid, so that the users can feel the resistance smooth and natural, which is essential for both comfort and effective exercise.
In essence, the flywheel serves as an energy storage device within the mechanical system. Unlike purely static resistance systems, an elliptical machine operates under continuously changing human input. The flywheel stabilizes this variability by converting intermittent human force into a more uniform rotational motion. This is why machines with insufficient flywheel performance often feel “choppy” or mechanically disconnected from the user.
Rotation Kinetic Energy — Ek
In an elliptical machine, a certain level of Rotation Kinetic Energy (Ek) must be maintained in the flywheel to ensure smooth, continuous motion throughout the pedal cycle.
From a physics perspective, rotational kinetic energy is the direct equivalent of linear kinetic energy in a moving object. Just as a moving mass carries momentum forward, a rotating flywheel carries angular momentum through the pedal cycle. This is particularly important in an elliptical machine because human force is not constant. The biomechanics of pedaling naturally produce peaks and valleys of force. The flywheel’s stored energy bridges these gaps, allowing the system to behave as if it were driven by a more constant input source.As the user applies force unevenly—stronger in some phases and weaker at the top and bottom of the stroke — the stored energy in the rotating system carries the motion through these low-force regions, preventing jerky or interrupted movement. This energy (Ek) acts as a buffer, absorbing input when force is high and releasing it when force drops, resulting in a consistent and stable feel.
If the Ek is too low, the motion becomes uneven and requires constant effort to sustain; if sufficient Ek is maintained, the system feels fluid and natural, which is essential for both comfort and effective exercise.
Parameters Affecting Ek
The rotation kinetic energy Ek is calculated as
Ek = ½ Iω2
I = mr2 — Inertia
r — radius of flywheel
For an elliptical machine, the Ek of the flywheel is affected by its mass, radius and the rotation speed.
This relationship reveals an important engineering insight:
- Increasing mass (m) or radius (r) increases inertia linearly or quadratically
- Increasing angular speed (ω) increases energy quadratically.
This means that angular speed is the most powerful parameter for increasing rotational kinetic energy. A relatively small increase in speed can compensate for a large reduction in mass or size.
Principle for an Optimal Design ...
In practical design, there are trade-offs associated with each parameter:
- Increasing mass improves stability but adds weight, cost, and structural demand
- Increasing radius enlarges the machine footprint and affects packaging
- Increasing speed introduces higher mechanical complexity, stress, noise, and precision requirements
Therefore, an optimal design is not about maximizing a single parameter, but about balancing all three to achieve the designed applications and desired user experience.
LB007 vs Traditional Elliptical Machine
Traditional elliptical machines rely on large (big r) and heavy (big m) flywheels to maintain the required Ek through a single-stage transmission. This approach depends primarily on mass and size to stabilize motion. While mechanically straightforward, it results in machines that are bulkier, heavier, and less efficient in terms of material use.
LB007, in contrast, achieves the required Ek by operating the flywheel at a significantly higher rotational speed. This allows the system to deliver the same smoothing effect with a much smaller and lighter flywheel, reducing overall size and weight without compromising motion quality.
To enable this, LB007 uses a two-stage transmission system with a 1:16 ratio, progressively increasing the rotational speed from the pedal input to the flywheel. This design shifts the system from a mass-driven approach to a speed-amplified approach. While a two-stage transmission introduces greater mechanical complexity and requires higher precision in components and assembly, it allows for a more compact and efficient overall design.
For comparison, a mid-range traditional elliptical machine typically uses a 20–30 lb flywheel, whereas the flywheel in LB007 is only 5 lb. Despite this large difference in mass, the higher rotational speed enables LB007 to achieve sufficient rotational kinetic energy for smooth and continuous motion.
From an engineering standpoint, this represents a more optimized use of physical principles—leveraging angular velocity rather than relying solely on mass—resulting in a machine that is more compact, efficient, and responsive.