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- Ran into a problem regarding a contradiction between my measurements and my calculations, which led to unexpected Magnus Force values.

Hello,

I'm currently doing a school essay on the Magnus Effect, but I'm having a problem regarding a contradiction between my measurements and calculations.

The experiment consists of letting go of rolled A4 paper cylinders on top of a ramp set on a table so that when the cylinder rolls down off the ramp and becomes airborne, it will have a spinning motion and be displaced under the table due to the Magnus effect. My experiment consisted of radius as the independent variable and horizontal displacement under the table as the dependent variable (mass is the same for all). A side view of the experiment looks something like this:

When I did the experiment, The cylinder with the largest radius got displaced back the furthest, resulting in a large horizontal displacement, and so it could be implied that the largest cylinder visually had the most noticeable Magnus Effect, and thus, the largest Magnus Force, right? The same applies to the smallest cylinder; the smallest cylinder barely got displaced under the table and looked more like it just fell off due to its higher velocity, thus resulting in very little horizontal deviation and not much of a noticeable Magnus Effect at all. A conclusion for this would be that the larger the radius, the larger the horizontal displacement, and thus, the larger the Magnus Force.

However, when I did the actual Magnus Force calculations, the opposite became true. The cylinder with the largest radius turned out to have the least Magnus Force, while the cylinder with the smallest radius had the largest Magnus Force. How could this happen?

The formula I used for the Magnus force was:

L = ρ⋅v⋅(2πr)^2⋅f⋅l

L is the Magnus Force in N

ρ is the density of the surrounding fluid in kg/m^3

v is the velocity of the projectile in m/s

r is the radius of the cylinder in m

f is the angular velocity of the cylinder in rad/s

l is the length of the cylinder in m

Here are the calculations for the largest cylinder, and smallest cylinder, respectively:

1.2754 ⋅ 1.5009 ⋅ (2π0.045)^2 ⋅ 33.4 ⋅ 0.21 = 1.073 N

1.2754 ⋅ 2.9907 ⋅ (2π0.025)^2 ⋅ 119.6 ⋅ 0.21 = 2.368 N

The only explanation I can think of is that since the radius value changed by such a small proportion, and the angular velocity changed by a much larger proportion, the angular velocity increase outweighed the radius decrease. So my guess is that it happened due to the formula's limitations. My teacher said he kind of ran out of ideas, any help would be greatly appreciated.

Thanks.

I'm currently doing a school essay on the Magnus Effect, but I'm having a problem regarding a contradiction between my measurements and calculations.

The experiment consists of letting go of rolled A4 paper cylinders on top of a ramp set on a table so that when the cylinder rolls down off the ramp and becomes airborne, it will have a spinning motion and be displaced under the table due to the Magnus effect. My experiment consisted of radius as the independent variable and horizontal displacement under the table as the dependent variable (mass is the same for all). A side view of the experiment looks something like this:

When I did the experiment, The cylinder with the largest radius got displaced back the furthest, resulting in a large horizontal displacement, and so it could be implied that the largest cylinder visually had the most noticeable Magnus Effect, and thus, the largest Magnus Force, right? The same applies to the smallest cylinder; the smallest cylinder barely got displaced under the table and looked more like it just fell off due to its higher velocity, thus resulting in very little horizontal deviation and not much of a noticeable Magnus Effect at all. A conclusion for this would be that the larger the radius, the larger the horizontal displacement, and thus, the larger the Magnus Force.

However, when I did the actual Magnus Force calculations, the opposite became true. The cylinder with the largest radius turned out to have the least Magnus Force, while the cylinder with the smallest radius had the largest Magnus Force. How could this happen?

The formula I used for the Magnus force was:

L = ρ⋅v⋅(2πr)^2⋅f⋅l

L is the Magnus Force in N

ρ is the density of the surrounding fluid in kg/m^3

v is the velocity of the projectile in m/s

r is the radius of the cylinder in m

f is the angular velocity of the cylinder in rad/s

l is the length of the cylinder in m

Here are the calculations for the largest cylinder, and smallest cylinder, respectively:

1.2754 ⋅ 1.5009 ⋅ (2π0.045)^2 ⋅ 33.4 ⋅ 0.21 = 1.073 N

1.2754 ⋅ 2.9907 ⋅ (2π0.025)^2 ⋅ 119.6 ⋅ 0.21 = 2.368 N

The only explanation I can think of is that since the radius value changed by such a small proportion, and the angular velocity changed by a much larger proportion, the angular velocity increase outweighed the radius decrease. So my guess is that it happened due to the formula's limitations. My teacher said he kind of ran out of ideas, any help would be greatly appreciated.

Thanks.