suri final paper
TRANSCRIPT
SURI Final Paper
Gauss Rifle
Instructor: Wilbur Dale
Cadets: Thomas Carnes and Adam Woloshuk
Summer 2009
I. Introduction:
Adam and I were first introduced to the idea of an electronic weapons system in EE-222
with Col. Squire. Col. Squire had brought one of his many toys to class one day and was
demonstrating all the exciting things an electrical engineer can build. This particular devise was
a ring-tosser of which a washer was attached to a rod, the rod was charged and the ring flew off.
Col. Squire said that there was a capacitor on E-Bay that he could get for around $40 that if used,
could project the ring into orbit. Adam and I immediately looked at each other and knew we
would like to do something like that.
We thought that weapons using gun powder, though very popular and efficient, were not
the only option to use as firearms, especially with the advances in electronics. The fact that
weapons using chemical energy (gun powder) are limited by the speed of sound, while electronic
devices, in theory are limited by the speed of light, posed as an option for new types of weapons.
When gun powder was first implemented in weapons during the Middle Ages, they were
inaccurate, dangerous, bulky, and inefficient. As history has shown, the gun-powder weapons
evolved from crude ineffective weapons into elegant, effective weapons. That was our hope for
this project, not to revolutionize weapons overnight, but perhaps provide the groundwork that
lead to an evolution in firearms.
We approached Maj. Dale about a SURI project to design an electronic weapons system.
Maj. Dale suggested that there were two feasible options, a rail gun type system or a gauss
system. We decided upon the gauss system, because the rail-gun’s barrel was known the wear
down very quickly due to friction, while the gauss system did not. Maj. Dale agreed to become
our advisor for the project, but we still needed to get approval from the SURI board. In order to
gain approval, we submitted a proposal listing why we were doing the project, the materials and
funding needed, as well as our objectives. Our objectives for the end of the project were to: gain
data from different experiments with our rifle, and ultimately to produce a working prototype of
our gauss rifle. After a few weeks, SURI granted us approval to start our project. We officially
started May 19, 2009.
II. Background:
The whole concept of our gauss rifle is that if we pass current through a coil (inductor), a
magnetic field will be generated. If we could harvest that magnetic field to apply a force on a
projectile, we could use that force to suck the projectile through our barrel and propel it out of
the other end (muzzle), giving us a shooting effect. One of the most fundamental concepts used
in the experiment was current flowing through a wire produces a magnetic field. We then
needed to use this fact to somehow derive an equation that gives us an idea of the force acting on
the projectile. To do this, we went back to the fundamentals of inductance:
, where is magnetic flux, L is the inductance, and i is the current.
.
If we combine these we can derive an equation for the power generated by the magnetic
field and mechanical power:
, with p being the power in the system, v is the voltage and i is the current. Now
substituting the
into the v in , we are left with
Using reverse
expansion of the product rule of derivatives, we obtain
=
.→
=
Finally,
The
portion of the
equation is the power flowing into the magnetic field, while the is the
mechanical power flowing into the projectile. This brings us to another important point: energy
in is equal to the mechanical energy plus the electromagnetic energy.
Now that we have our equation for power, we can derive an equation for force:
where pm is mechanical power, F is the force on the projectile, and ds/dt is
the velocity of the projectile.
by the chain rule we conclude
This equation states that force (N) is equal to half the current (A) squared multiplied by
the derivative of inductance (H) with respect to position (m). This is the formula on which we
will base the rest of the experiments. As measured in the lab, once the projectile passes through
the center of a coil, the derivative will be negative. If the derivative is negative, then we will
have negative forces acting against the projectile, propelling back towards us. We would to
design a timing circuit to shut off the current once the projectile has reached the half way point
of each inductor. We also need to design a firing sequence and detection circuit to signal the
firing for each coil.
Another point of consideration was the design of our inductors. We needed to determine
the most effective way of designing each coil. We were unsure whether it would be best to use
single stacked with a constant number of turns for our coil, or coils stacked on top of one another
with a constant number of turns. Maj. Dale had a reference of a semi-empirical equation that
suggested that the inductance was related to the height and width of the inductor, and inductance
reached a peak as the limit of height and width grew relatively equal in size. This is needed to be
tested.
III. Preliminary Work:
Based upon the data obtained in the experiments, we have chosen to use the ten stacked
geometry because its offers the overall highest derivative. With our inductor issue settled, we
need to start designing a circuit for our rifle.
Above is the basic circuit of our rifle, L is our coil (inductor), R is the resistance of the projectile
entering the coil, and C is the capacitor. Now it becomes necessary to derive a series of
equations for the natural response of the circuit. Using methods learned during EE-223 we are
able to derive the following equations:
.
Substituting the equations we have:
.
Using the definitions of inductance and capacitance:
. And
.
We are now able to solve for our circuit:
Therefore based upon the above calculations, we should end up using an under damped
function for our current. This is because the switch requires our current to go to zero to avoid
arcing destroying the electrical switch. When current goes to zero, force,
goes
to zero, past that it becomes negative.
The above relationship will cause the current function to be under damped.
Now that we have solved the differential equations for our circuit, it becomes necessary
to develop a system of equations for various components and values essential to our circuit.
One of the most important equations we need to derive is that of, , the average current
squared:
Now that we have an equation for our average current squared, we now have a stepping stone for
solving the values of other variables such as capacitance, period, initial voltage, and energy.
Solving for capacitance we have:
The above diagram is the circuit that we used for the light-detection circuit. Using an infrared
LED and a light-sensitive diode, we were able shoot the beam from the LED through the barrel.
Thus, when the projectile broke the beam, the next inductor would fire.
R2
1.5k
R3
15k
R4
56k
R5
56k
R6
560
U1A
LM393
3 +
2-
V+8
V-4
OUT1
Q1
D1
D2
0
The above diagram is the circuit that we designed to handle the firing sequence. When the signal
from the light detection circuit went high, the firing sequence activates and fires the next coil on
the barrel.
IV. Experimental Work:
Our work on the project began with collecting data on different types of solenoids.
In our initial experiments we kept the number of turns in each solenoid constant at 240 turns, changing
the number of stacks and the number of turns in each stack. By maintaining a constant number of total
we were able to determine the best solenoid to use in order to optimize the usable barrel space and the
force on the projectile.
Our procedure consisted of hand coiling each solenoid on the barrel, and then measuring the
change in inductance as the projectile passed through the barrel. This allowed us to determine
V1
12Vdc
R1
1.0k
2.632mA
R2
3.9kRE
330
0
0
Q1
Q2N3906
Q2
Q2N3904 R4
10kSignal
11Vdc
0
the derivative of each separate solenoid, combining the derivative and the velocity of the
projectile in the barrel gave us the force working on the projectile, which also gave us the
equivalent resistance of the projectile as it moved through the barrel. These values helped us to
eliminate more of the unknowns in our equations.
We repeated these steps for each solenoid, starting with a single stack with 240 turns and
continuing to make solenoids that were stacked by each number up to twelve that evenly divides
240. The number of stacks we collected data on was limited to twelve due to the data starting to
plateau.
After collecting the data on the solenoids, we moved onto seeing the effects of different size
projectiles in the same solenoid. We tripled the size of the projectile and found that there was a
significant increase in the inductance, and therefore the derivative, in the same solenoid. This
led us to using a larger projectile with a shorter, but higher stacked, coils. By approaching it in
this way we were able to have the projectile be situated in such a way that it would be in the
magnetic field of two of the solenoids, combined with the firing circuit, we determined that this
would allow us to be firing two of the solenoids at a time while keeping the projectile in the first
third of the magnetic field, thus optimizing both the amount of barrel being used and the amount
of force being applied to the projectile.
V. Results:
As indicated by the chart below, as the number of stacks increases not only does the overall
derivative increase, but as the number of stacks approaches the number of turns a the derivative
as the projectile moves through the first third of the coil spikes.
This spike in the derivative is what indicated to us that the optimal force is created while the projectile
moves through the first third of the solenoid. From the data we received from the experiments with the
solenoids, combined with the equations we had derived, we were able to produce the following
information.
0
200
400
600
800
1000
1200
1400
1600
0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000
Y (
uH
)
X (cm)
Inductor Data
10x Stacked 24 Turns Each (240 Total Turns)
6x Stacked 40 Turns Each (240 Total Turns)
4x Stacked 60 Turns Each (240 Total Turns)
Triple Stacked 80 Turns Each (240 Total Turns)
Double Stacked 120 Turns Each (240 Total Turns)
Single Stacked 240 turns
# of stacks 10 # of turns per stack 10
Inductance
Forceproj
Lcenter 0.000306
G-Force 25
sint 0
Lstart 0.000266
Dcoil 0.015
sfin 0.015
Laverage 0.000286
a 245.25
tint 0
S 0.025
mproj 0.0225
tfin 0.01106
dl/ds 0.0016
vint 0
vfin 2.712471
Derivations
Tper 0.000369
R 0.001084988
Tacc 0.01106
1.896833006
Burst 30
567.8106374
E 0.082772
C 1.20494E-05
V0 19.28381
I 83.05212971
<i
2> 6897.656
<dS/dt> 1.356236
This spreadsheet shows all of the unknowns that were solved for the first of the five coils. The next five sheets show the data for each coil
respectively, the last being the fifth and final coil which has two data sheets due to it having two sets of equations, one while the fourth coil is
firing in conjunction with the fifth and one while the fifth is being fired on its own.
# of stacks 10 # of turns per stack 10
Inductance
Forceproj
Lcenter 0.000306
G-Force 25
sint 0
Lstart 0.000266
Dcoil 0.03
sfin 0.03
Laverage 0.000286
a 245.25
tint 0
S 0.025
mproj 0.0225
tfin 0.015641
dl/ds 0.0016
vint 0
vfin 3.836014
Derivations
Tper 0.000372
R 0.001534405
Tacc 0.015641
2.682526962
Burst 42
401.5027522
E 0.165544
C 1.22936E-05
V0 13.77775
I 83.05212971
<i
2> 6897.656
<dS/dt> 1.918007
# of stacks 10 # of turns per stack 10
Inductance
Forceproj
Lcenter 0.000306
G-Force 25
sint 0.015
Lstart 0.000266
Dcoil 0.03
sfin 0.045
Laverage 0.000286
a 245.25
tint 0.01106
S 0.025
mproj 0.0225
tfin 0.019157
dl/ds 0.0016
vint 2.712471
vfin 4.698138
Derivations
Tper 0.000368
R 0.002964244
Tacc 0.008097
5.182244145
Burst 22
775.6437553
E 0.165544
C 1.20057E-05
V0 26.61656
I 83.05212971
<i
2> 6897.656
<dS/dt> 3.705305
# of stacks 10 # of turns per stack 10
Inductance
Forceproj
Lcenter 0.000306
G-Force 25
sint 0.03
Lstart 0.000266
Dcoil 0.03
sfin 0.06
Laverage 0.000286
a 245.25
tint 0.015641
S 0.025
mproj 0.0225
tfin 0.02212
dl/ds 0.0016
vint 3.836014
vfin 5.424942
Derivations
Tper 0.00036
R 0.003704382
Tacc 0.006479
6.476192973
Burst 18
969.3133896
E 0.165544
C 1.14837E-05
V0 33.26243
I 83.05212971
<i
2> 6897.656
<dS/dt> 4.630478
# of stacks 10 # of turns per stack 10
Inductance
Forceproj
Lcenter 0.000306
G-Force 25
sint 0.045
Lstart 0.000266
Dcoil 0.03
sfin 0.06
Laverage 0.000286
a 245.25
tint 0.019157
S 0.025
mproj 0.0225
tfin 0.02212
dl/ds 0.0016
vint 4.698138
vfin 5.424942
Derivations
Tper 0.00037
R 0.004049232
Tacc 0.002964
7.07907715
Burst 8
2119.098148
E 0.082772
C 1.21656E-05
V0 71.96814
I 83.05212971
<i
2> 6897.656
<dS/dt> 5.06154
# of stacks 10 # of turns per stack 10
Inductance
Forceproj
Lcenter 0.000306
G-Force 25
sint 0.06
Lstart 0.000266
Dcoil 0.03
sfin 0.075
Laverage 0.000286
a 122.625
tint 0.031282
S 0.025
mproj 0.045
tfin 0.034975
dl/ds 0.0016
vint 3.836014
vfin 4.288794
Derivations
Tper 0.000369
R 0.003249923
Tacc 0.003692
5.681683281
Burst 10
1700.792951
E 0.082772
C 1.20868E-05
V0 57.76179
I 83.05212971
<i
2> 6897.656
<dS/dt> 4.062404
By using these spreadsheets we were able to determine the size of the capacitor that we
would need to use, the initial voltage that each capacitor would need to be charged to, and the
current that would the system would need to be able to sustain. All of this data allowed us to
begin building a prototype and start the next phase of testing, which is to test the actual firing
circuitry. During the course of these experiments, we tested a six stacked coil with 3.9 A of
current running through it, not only did it suck the projectile into the barrel, but when we held the
barrel vertical there was enough force acting on the projectile to levitate it in the middle of the
coil.
VI. Conclusions:
The results that we have thus far achieved have shown us that our idea, the concept of a
Gauss rifle, is a viable one. We have found that there will need to be some modifications done to
make our rifle completely weaponized, though the modifications could be done with further
research. Although we were unable to complete the rifle during our SURI, we have plans to
continue the research in the future. Even though we were unable to complete the rifle, we feel
that we have made progress into a new form of firearm, one that could change the way guns are
fired forever.