Force Calculation of Office Chairs
The force calculation of office chairs mainly includes the chair's own gravity, the pressure on the seat cushion when a person sits upright/leans back, and the pressure on the ground exerted by the chair. The specific calculations are as follows:
Chair's Own Gravity
The gravity of a chair is determined by its mass, calculated using the formula $G = mg$ ($G$ is gravity, $m$ is mass, and $g$ is the acceleration due to gravity, typically taken as $10\ \text{N/kg}$). If the chair has a mass of $10\ \text{kg}$, its gravity is:
$$G_{chair} = 10\ \text{kg} \times 10\ \text{N/kg} = 100\ \text{N}$$
This result reflects the basic force exerted by the chair on the supporting surface when it is stationary.
Pressure on the Seat Cushion When Sitting Upright
When a person sits upright, the pressure $F$ on the seat cushion is usually taken as the vertical force exerted by the human body on the cushion (e.g., $320\ \text{N}$), and the contact area $S$ is the effective area where the cushion touches the human body (e.g., $8 \times 102$). According to the pressure formula $p = \frac{F}{S}$, the pressure when sitting upright is:
$$p_1 = \frac{320\ \text{N}}{8 \times 102} = 4000\ \text{Pa}$$
The higher the pressure, the stronger the force per unit area. When sitting upright, the local force on the human body is more concentrated, which may cause discomfort.
Pressure on the Seat Cushion When Leaning Back
When leaning back, the human body's weight is distributed between the backrest and the seat cushion, reducing the pressure on the cushion and thus lowering the pressure. If the pressure when leaning back is $p_2 = 2000\ \text{Pa}$, comparing it with the pressure when sitting upright shows:
$$p_2 < p_1$$
A decrease in pressure means a reduction in the force per unit area, resulting in a more even distribution of pressure on the human body. Therefore, the leaning-back posture is generally more comfortable.
Pressure on the Ground Exerted by the Chair
The total pressure on the ground exerted by the chair is the sum of the chair's gravity and the pressure exerted by the person on the seat cushion, i.e.:
$$F_{total} = 320\ \text{N} + 100\ \text{N} = 420\ \text{N}$$
If the chair has 5 wheels and the contact area of each wheel is $4 \times 102$, the total contact area is:
$$S_{total} = 4 \times 102 \times 5 = 2 \times 102$$
According to the pressure formula, the pressure on the ground exerted by the chair is:
$$p_{ground} = \frac{F_{total}}{S_{total}} = \frac{420\ \text{N}}{2 \times 102} = 2.1 \times 10^5\ \text{Pa}$$
This result reflects the concentrated force exerted by the chair on the ground through its wheels. Although the pressure value is high, the rolling design of the wheels effectively disperses the pressure, preventing damage to the ground.
