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Analysis of table tennis track

Fit the data obtained from the Eagle Eye system to get the speed, use Newton's law and fluid mechanics to get a table tennis motion model, and predict future movements!

Movement problem analysis:

There are three main forces in table tennis after the player's shot:

(1) Gravity G mg, will always be affected by gravity during the entire flight, the direction of gravity is vertical downward;

(2) Air resistance FR, table tennis diameter is D, rotation angular velocity is, air viscosity coefficient is (see Table 1),

The air density is, the speed at which the table tennis moves forward is v, and the size of the air resistance to the table tennis is mainly determined by the Reynolds number Re and the translation speed v; If the Reynolds numbers of two geometrically similar flow fields are equal, then the ratio of inertial force and viscous force of the corresponding micelles is equal. The smaller the Reynolds number means the more significant the effect of the viscous force, the greater the greater the effect of the inertial force. Flows with a small Reynolds number (such as those in a lubricating film) have viscous effects throughout the entire flow field. For flows with a large Reynolds number (such as general aircraft flow), its viscosity effect is only important in the boundary layer or wake near the object surface.

Re Dv

Temperature (oC) viscosity coefficient

617.2 100

61017.8 10 Table 1 Viscosity coefficients at different temperatures

2018.3 10

3018.7 10 6

4019.2 10 6

5019.6 10 6

6020.1 10 6

We take room temperature as 10oC, so the viscosity coefficient is 17.8 10, = 1.205kg / m 3, 6 6

So we first calculate the Reynolds number for table tennis:

Re vD some value

The resistance FR is proportional to the square of the translational speed.

FR 1C Av2, 2

A is the cross-sectional area of table tennis

CD is the resistance coefficient. According to the range of different Reynolds numbers, there are

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