Info on forces and strains required and produced

How much force is required?

• Pressure and friction drag forces act to slow the fish as it moves

• The muscles, in order to move the fins, must overcome:– Pressure drag of the fin due to rotation– Pressure drag on the fin due to apparent incoming fluid

velocity– Reactions from the other fins– Friction drag slows the fish, but is NEGLIGIBLE as far as

muscle force is concerned

Preliminary pressure drag calculations

Preliminary pressure drag calculations

• The pressure drag force is dependent on the perpendicular velocity squared.

• The torque is found by integrating the drag force times distance along the fin section.

𝑇=∫0

𝑙

𝑑𝑇=∫0

𝑙

𝑥∗ 𝑑𝐹=𝜌 𝐶𝐷h2

∫0

𝑙

𝑉 𝑝𝑒𝑟𝑝2 𝑥𝑑𝑥

Preliminary pressure drag calculations

• are constants, either from dynamic simulation, or assumed as worst case

• Final equation for pressure drag:

𝑇=𝜌𝐶𝐷h2 (𝜔2 𝑙4

4−2𝜔2𝑎 𝑙3

3+𝜔

2𝑎2𝑙2

2+2𝜔𝑙3𝑣 h𝑓𝑖𝑠 sin (𝜃 )

3−𝜔𝑎 𝑙2𝑣 h𝑓𝑖𝑠 sin (𝜃 )+

𝑙2𝑣 h𝑓𝑖𝑠2 sin2 (𝜃 )2 )

Preliminary pressure drag calculations• Worst case parameters:

– (period of oscillation of 2 seconds)– square tail section long and high

– (a fixed pivot point)– ( for a closed C-shape)

• Torque due to pressure drag is • Crude approximation of drag force produced a torque of ,

as an error check against the more detailed calculation (agrees to the extent expected).

• With a level arm of 4cm, the force required to overcome the pressure drag is 1.83 pounds.

Muscle testing

• Insert picture of muscle tester setup here

1st round of muscle testing – lessons learned

Dead zone due to space between tubing and fabric mesh. 30 psi was the pressure required to take up the initial slack between the tubing and mesh.

Slope inversely related to rubber stiffness, and directly related to the ratio of inner circumference over wall thickness

2nd round of muscle testing

• Assembled new muscles with existing tubing and fabric mesh.

• Used tubing with high inner circumference to thickness ratio (it was thinner).

• Made sure there was no space between tubing and mesh.

• Tested the effect of using a slightly smaller mesh than needed, on the same tubing.

2nd round of muscle testing

• Tighter mesh nearly eliminated the dead zone• Obtained a force of approximately 4 pounds at 20psi

• No significant difference between mesh types as long as they’re tight against the tubing

2nd round of muscle testing

Force Feasibility

• Force required due to overcome pressure drag with a muscle lever arm of 4cm (1.57”): 1.83 pounds

• Force produced by first set of muscles: 4 pounds• Reaction forces from other fin sections are significant,

but also actuate out-of-phase. Are ultimately due to the drag as well, so should be on the same order.

• Clearly within feasibility, using a muscle assembled from a limited selection of scrap materials.

Strain feasibility

• Strain level of 13% at 20psi found during testing.• A lever arm of 4cm, and maximum angle of 30°,

requires a 30.8cm (12.2”) muscle– Has to actuate the section 30°, as well as

accommodate 30° of motion in the other direction

• Larger muscles can be used, making it possible to move lower the lever arm length, decreasing the required muscle length.

Show pictures of fish to CAD model

• Side view of CAD model, and real bass• Same for front view (aspect ratio) (maybe on a

separate slide)• Also show video of Essex fish; say that we’re

going to have the muscles execute a similar motion.

• Same argument for forward motion at this point.