Command, Control, and Monitoring Technologies
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Research and Technology 2002
 
Solenoid Inter-Force (SIF) Calculator
 
The Lorentz force is the well-known force exerted on a charged particle of charge q and velocity v in a magnetic field B:  

The final force formula given in figure 2 is found by combining Equations (3) and (4). This is the force that pushes coil 2 above coil 1 while balancing gravity. The levitation height h is dependent on the product of the currents in both coils (I1 and I2) as well as the mass of coil 2. Note that if the currents I1 and I2 flow in the same direction, the force is attractive. In order to levitate, the currents must be in opposite directions.


The height h in figure 1 was measured for several values of current. For this data, currents were equal and opposite. This data is shown in the plot of figure 3 as circles. Results are also plotted from the SIF calculator for the same range of current values (figure 4). Even though the calculated and measured values are not exactly lined up, the correlation suggests that the SIF calculation produces reasonable results.


Key accomplishments:

  • Developed an analytic formula to calculate the levitation height between two solenoids constrained to move in the axial direction.
  • A Windows calculator was developed that evaluates levitation height based on input coil parameters, as well as estimates of coil temperature.
  • Using similar analytic methods, a formula that computes theapproximate current leading to mechanical failure (coil implosion) was derived.

 

 

Contacts: Dr. R.C. Youngquist (Robert.Youngquist1@ksc.nasa.gov), YA-C3-E, (321) 867-1829; and Dr. J.C. Simpson, YA-D7, (321) 867-6937
Participating Organization: Dynacs Inc. (Dr. J.E. Lane and Dr. C.D. Immer)

Lorentz force
  

When a charged particle, such as an electron or proton with a linear velocity, encounters a magnetic field, the Lorentz force results in a spiral trajectory, where the circular portion of the path is perpendicular to the B field.

The integral form of the Lorentz force equation is:

  
integral form of the Lorentz force
  
Equation (2) is useful in describing a solenoid coil configuration. This is the case in figure 1, where the bottom coil (coil 1) is stationary and has a steady-state current of I1. The upper coil (coil 2) in figure 1, which has a steady-state current I2, slides along a vertical rod, maintaining axial symmetry.

A form of the force equation that lends itself to evaluation by computer is:
  
A form of the force equation that lends itself to evaluation by computer
  
where I2 is the current and A2 is the cross-sectional area of coil 2 wire, ak is the radius of the kth wire loop of coil 2, and Bk is the field at the position of the kth wire loop of coil 2. The position of the kth wire loop is specified by rho equals ak and z = zk.

Now sum the simple analytic expressions for the magnetic field of a circular current loop over all loops of the solenoid (see “Solenoid Inductance and B-Field Calculator,” KSC Research and Technology 2000-2001 Report):
  
A sum of the simple analytic expressions for the magnetic field of a circular current loop over all loops of the solenoid
  

The final force formula given in figure 2 is found by combining Equations (3) and (4). This is the force that pushes coil 2 above coil 1 while balancing gravity. The levitation height h is dependent on the product of the currents in both coils (I1 and I2) as well as the mass of coil 2. Note that if the currents I1 and I2 flow in the same direction, the force is attractive. In order to levitate, the currents must be in opposite directions.


  

Lorentz Levitation Test

Figure 1. Lorentz Levitation Test

 

SIF Analytic Formulas

Figure 2. SIF Analytic Formulas

  

Measured Versus Calculated Data

Figure 3. Measured Versus Calculated Data

 

SIF Windows Panel

Figure 4. SIF Windows Panel
     
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