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The University of Akron
Re-Heating Travel Mug
Honors Senior Project
Rachel Weyand
April 13, 2011
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Table of Contents
Design Process………………………………………………………………………………….4
Material Selection………………………………………………………………………………5
Cup Geometry………………………………………………………………………………….11
Heat Transfer Analysis…………………………………………………………………………12
Thermal Testing………………………………………………………………………………..18
Motor Testing…………………………………………………………………………………..23
Concluding Remarks…………………………………………………………………………...28
Works Cited…………………………………………………………………………………....29
Appendices…………………………………………………………………………………30-39
Appendix A- Original Proposal………………………………………………………..30
Appendix B- Semester Status Update………………………………………………....31
Appendix C- Raw Data for Thermal Testing…………………………………………..34
Appendix D-Raw Data for Motor Testing……………………………………………..39
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Design Process
The design process for any new system starts with a market need and ends with the full
specification of a product that fills the need or embodies the idea. Below in figure 1 from
Michael Ashby’s book Material Selection in Mechanical Design is shown that after there is a
market need, we need to break down the process by concept, embodiment and detail before
getting to the end product (Ashby, 2011).
Figure 1
For our project we started with the idea of a self heating travel mug that would be capable
of maintaining a heated beverage by means of insulation and an internal heating mechanism that
would not need to be plugged in to reheat. We evaluated and researched ideas that may or may
not work in our concept. Our original idea was to use magnetic induction to heat our coffee. This
idea we found from the flashlights that you shake to produce enough energy to light an LED
light. These flashlights had a cylinder magnet and coils that surrounded the magnet. When the
magnet passes through the coils it produces energy that is stored in the capacitor shown below in
figure 2.
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Figure 2
We bought flashlights and from research and talking with professors in the electrical
engineering department of the University of Akron, we found that we would not produce enough
energy to heat or even to maintain the heat for our travel mug. The cylindrical magnets were
losing energy because they had to travel a distance through the flashlight that wasn’t totally
surrounded with coils. So the magnet was not producing energy at the bottom and top of its
revolutions. We had to take a step back and rethink an idea where we could gain more energy
than what were produced in the flashlights. Next we thought of spinning the magnet in a circular
motion and surrounding it with coils to get more energy than before. Even with this idea we
wouldn’t be able to produce enough energy.
Again we took a step back to the concept part of the mechanical design process and we
realized that using a motor or generator would help us to produce enough energy for the heater.
We still did not want to plug in the coffee cup, so we knew we had to design a gearing system
where the user could input energy to turn the motor and in turn give energy to the heater to heat
the coffee mug.
Material Selection
In choosing a material, one must establish the link between the material and its function.
Michael Ashby is quoted in the book Material Selection in Mechanical Design on page 98
saying, “The task of selection, stated in two lines, is that of
1. identifying the desired attribute profile, and then
2. comparing this with those of real engineering materials to find the best match.”
The system is broken into four categories by Ashby into translation, screening, ranking and
seeking documentation before you can choose the final material. As shown below in figure 3
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from Ashby’s book, translation is the first step and can be broken down into finding the function,
constraints, objective, and free variables.
Figure 3
Screening the materials using the constraints is the next step, where elimination of
materials that cannot do job are thrown out. Following the screening step, the remaining
materials should be ranked to find which materials can do the job the best. The final step is to
seek documentation of those materials that are left. Research should be done to find family
history of the top-ranked materials.
When looking into the translation step of the material selection process, it can be broken
down into function, constraints, objective, and free variables. These are then broken down in
figure 4 from Ashby’s book below into the questions that need to be asked in order to move onto
the next step of the selection process.
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Figure 4
In our project we have several components that need to go through this process in order
to find the best and most cost efficient material for each component, which in turn will give us
the best system possible from the material standpoint. Our list of components that needs to go
through the material selection process is our inside liner, insulation, and outside liner.
To start off, we first looked at the inside liner and answered the questions in the
translation part of the selection. The inside liner’s function is to hold the hot beverage (about
135°F) and our constraints are that it must be food safe and must transmit heat. The objectives of
the inner liner are that we want to maximize thermal conductivity and thermal diffusivity and
also to minimize cost. Thermal conductivity is the material property governing the flow of heat
through a material at steady state. Since our heater is surrounding our inner liner we want to have
a high thermal conductivity to ensure that we can get the most heat to our liquid. Thermal
conductivity is measured in Watts per meter Kelvin (W/m-K). Thermal diffusivity is the property
governing transient heat flow, which can be otherwise stated as thermal conductivity divided by
the volumetric heat capacity.
where k is the thermal conductivity (W/m-K), ρ is the density (kg/m^3) and is the
specific heat capacity (J/kg-K). Thermal diffusivity is measured in meters squared per Kelvin
. Materials with high thermal diffusivity rapidly adjusts their temperature to that of their
surroundings because they conduct heat quickly in comparison to their volumetric heat capacity
and they generally do not require much energy from their surroundings to reach thermal
equilibrium. The free variables for the inner liner are the choice of material. By looking at figure
5 below from Michael Ashby’s Material Selection in Mechanical Design book, we were able to
see that the top right of this chart is where we wanted to choose our material for the inside liner.
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Figure 5
Knowing that our inside liner must be food safe, we were able to eliminate copper, lead,
aluminum, zinc, and magnesium (FDA Food Code 2009). Because we were designing a travel
mug we knew it could be dropped at times, we didn’t want our product to easily be broken. This
eliminated the ceramics because they are brittle.
Material
Thermal
Conductivity
(W/m*K)
Thermal
Diffusivity
(m^2/s)
Cost/volume
Stainless Steel
16
40^-6
3rd cheapest
Cast Iron
40
10^-5
Cheapest
Carbon Steels
50
15^-5
2nd cheapest
20^-5
most
expensive
Nickel Alloys
80
Table 1
Even though looking at the data in table 1 above, the stainless steel might not have the
highest values for thermal conductivity and diffusivity, we still chose the stainless steel because
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it is already used for coffee mugs and it was able to be found very cheap for our prototype
application.
Our next component that was analyzed was the insulation. The function of the insulation
is to keep heat from leaving the system and its constraint is that it must keep heat in the system.
The objective of the insulation is just the opposite of the inside liner, where in this case we want
to minimize the thermal conductivity and thermal diffusivity, but we still want to minimize cost.
The reason we want to minimize the thermal conductivity and thermal diffusivity is because we
want the heat to stay in and with smaller values of thermal conductivity and diffusivity we can
keep the heat from leaving the system. The free variable for the insulation is also the choice of
material. By bringing back the figure on thermal conductivity and thermal diffusivity from the
Materials Selection in Mechanical Design book in figure 6 we can now want to look at the
materials in the bottom left corner of this chart.
Figure 6
We were able to find some foams, air, rubber and isoprene that were all towards the
lower left corner of figure 6. With looking at the data in table 2 found from a website titled
Thermal conductivity of Some Common Materials and from Ashby’s book, we thought at first in
our situation that air would be easy to use and free, but we realized we may lose some heat due
to radiation because the insulation is surrounding the heater and would not be a practical option.
Isoprene and butyl rubber are not as convenient because they have higher values of thermal
conductivity and are more expensive. The polyurethane would be the best choice since it has low
values in thermal conductivity and thermal diffusivity and is cheap, but in our prototype we
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chose a polyethylene foam insulation that has a similar thermal diffusivity and slightly higher
thermal conductivity. The polyethylene foam insulation was easily found in the correct thickness
and was also found to be inexpensive.
Polyurethane
Urethane
Air
Polyethylene
Foam insulation
Isoprene
Butyl Rubber
Thermal
Conductivity
(W/m*K)
0.02
0.021
Thermal
Diffusivity
(m^2/s)
10^-7
10^-7
0.02
0.03
0.13
0.09
10^-7
40^-8
50^-8
Table 2
Cost/volume
Cheapest
2nd Cheapest
Cheap but will cause
radiation
Cheap
More expensive
More expensive
The last component that was analyzed was the outside liner. Its function is to serve as a
protection layer to the coffee mug and also to serve as a second layer of insulation and keep heat
from leaving the system. Our constraints for the outside liner are that it must keep heat from
leaving the system and also must protect the inside cup when dropped. One other constraint we
added was to be transparent because we wanted to put a thermometer inside the cup to be
protected by the outside liner and to show the user the temperature of the coffee. The objective of
the outside liner of the coffee mug is similar to that of the insulation, where we want to minimize
the thermal conductivity, thermal diffusivity, and cost. The free variable is the same as the other
two components, where it is the choice of material. In continuing this process, figure 6 was used
again and the lower left hand corner is where we wanted our material to be. The foams that we
researched for the insulation would be impractical because we wanted a rigid outside liner that
would protect the inside contents of the cup, such as the heater, motor, spring, and gearing
system.
Thermal Conductivity Thermal Diffusivity
(W/m*K)
(m^2/s)
Cost/volume
PP
0.15
70^-8
Cheapest
PMMA
0.2
80^-8
3nd Cheapest
PVC
0.19
10^-7
2nd Cheapest
PC
0.21
12^-7
Table 3
More expensive
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From the data in table 3, polypropylene (PP) seems to be the best choice because it is the
cheapest and has the minimum thermal conductivity and second smallest thermal diffusivity, but
we couldn’t get this material to be transparent. So our next choice because of its transparent
properties was the polycarbonate (PC). We were also able to find this material for a decent price
considering it was considered the most expensive material in Michael Ashby’s book, Material
Selection in Mechanical Design.
The materials that we chose were narrowed down by the process of material selection are
as follows:
Inside cup liner: Stainless Steel
Insulation: Polyethylene foam insulation
Outside cup liner: Polycarbonate
Cup Geometry
We wanted this cup to still be able to fit in a normal coffee cup holder in cars, so it would
be easy to transport. After measuring a standard cup holder, we found the diameter to be just
over 3.5 inches. From there we wanted to design the outside diameter to be 3.5 inches. Below in
figure 7, the dimensions of our cup are shown.
Figure 7
The thickness of our outside layer is to be .125 inch, whereas the thickness of the
insulation layer will be 0.25 inch. Lastly the thickness of the inside cup layer is to be 0.125 inch,
which makes this inside diameter to be 2.5 inches. Shown below in figure 8 below, the height of
the inner liner, where the beverage will be held, is shown to be 5.88 inches. This was determined
based on our idea that we wanted the cup to hold 16 fluid ounces. The bottom 3 inches will be
used for storing our motor and gearing system.
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Figure 8
This was our original idea, and still is what we would want our final product to be, but
when looking for readily available materials, we weren’t able to fit to our first design. Our
biggest problem was finding a small motor that could produce high wattages(of about 120
Watts), but also have a low rpm rating. These motors were only available for expensive prices,
and for our prototype we wanted to prove that our idea worked and eventually we would be able
to design our own small motor that could be mass produced for less money. We were able to
obtain a motor that gave us enough wattage, but its size was much larger than we had hoped.
Heat Transfer Analysis
Our cup geometry was based on having a cup that would hold 16 fluid ounces, which is a
standard travel coffee mug size. We had to do a heat transfer analysis for two different scenarios.
Our first scenario is to find the energy required to maintain the heat in the cup whereas the
second scenario is to find the energy required to heat up the fluid.
Scenario 1
For the first scenario to find the heat that is leaving the system, we need to do conduction
through the sidewalls, conduction through the bottom and conduction through the lid. In the table
4 below here are all our values used to find the heat leaving the system.
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Given
Tamb
Tfinal
70
135
degF
degF
Volume
Diameter
Height
16
2.5
5.88
oz
inches
inches
Radius Layers
radius 1
radius 2
radius 3
radius 4
Height
Area
1.25
1.375
1.625
1.75
5.88
inches
inches
inches
inches
inches
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0.027
0.0263
0.5
W/m*K
W/m*K
W/m*K
W/m*K
Thermal Conductivites
SS
Insulation
air
plastic
294 K
330 K
I.cup wall thickness
Insulation thickness
O.cup wall thickness
0.032
0.035
0.041
0.044
0.149
0.015
0.125
0.25
0.125
inches
inches
inches
meters
meters
meters
meters
meters
m^2
Table 4
Starting with the conduction through the side walls, figure 9 below shows the resistances
through the sidewalls. Our acceptable coffee temperature is 135°F and we assumed our ambient
temperature to 70°F. The resistances through the sidewalls include the inner stainless steel cup,
the insulation liner, and the outer plastic cup.
Figure 9
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The equation used to find the heat lost through the sidewalls is as follows:
And to find the resistances for cylindrical geometries:
We found the resistance of the inner liner to be 0.007K/W, the resistance of the insulation
to be 6.597 K/W and the resistance of the outer cup to be 0.006K/W. After finding the
resistances, we were able to find that the heat lost through the sidewalls was about 5.5 Watts.
H/T Lost Through Sidewalls
R(inner cup)
R(insulation)
R(outer cup)
0.007
6.597
0.006
K/W
K/W
K/W
Qconduction-sidewalls
5.463 Watts
Table 5
Now moving on with the conduction through the bottom; the figure 10 below shows the
resistances through the bottom of the cup. The resistances through the bottom include the inner
stainless steel cup, the insulation liner, a layer of air, and the outer plastic cup.
Figure 10
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The equation used to find the heat lost through the bottom is as follows:
And to find the resistances:
We found the resistance of the inner liner to be 0.015K/W, the resistance of the insulation
to be 7.378K/W, the resistance of the air to be 189.369 and the resistance of the outer cup to be
0.015K/W. After finding the resistances, we were able to find that the heat lost through the
bottom was about 0.2 Watts.
H/T Lost Through Bottom
L1 cup thickness)
L2 insulation
L3 area with motor(air)
L4 cup thickness
R1 (I. cup)
R2 (Insulation)
R3 (air)
R4 (O. cup)
Qconduction bottom
0.003
0.003
0.076
0.003
m
m
m
m
0.015
7.378
189.369
0.015
K/m
K/m
K/m
K/m
0.184
Watts
Table 6
Lastly looking at the conduction through the top, the figure 11 below shows the
resistances through the top. There is only one resistance through the top which is the resistance
through the lid.
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Figure 11
The equation used to find the heat lost through the top is as follows:
And to find the resistances:
We found the resistance of the lid to be 2.047K/W. After finding the resistance, we were
able to find that the heat lost through the top was about 17.6 Watts. This gives us a total of 23.3
Watts of heat that are lost from the system.
H/T Lost Through Top
L1 (lid thickness)
Area
Resistance
Qcond. 3
0.006
0.006
2.047
17.640
m
m^2
K/m
Watts
Table 7
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Scenario 2
Scenario two was where we calculated the energy required to heat up the fluid. The
givens shown in table 8 below show the volume as 16 ounces and the density of coffee is 561
kg/m^3, which gives us a mass of 0.265 kg. The specific heat, , is 4184 J/kg*degK.
Volume
Density
Mass
Specific Heat
16
561
2.65E-01
4184
ounces
kg/m^3
kg
J/kg*degC
Table 8
Table 9 below shows different temperature scenarios to find how much energy we would
need to increase the temperature by that much. From there, we also took different time frames for
the beverage to increase to the desired temperature. With all this, we were able to find the power
that we would need to produce for different temperature deltas and different time frames.
Initial Temperature (F)
Initial Temperature C
Final Temperature (F)
Final Temperature C
Needed Energy (J)
Power (Watts)
2
3
4
5
6
7
8
9
10
(Time in Minutes)
70
21
135
57
40039
80
27
135
57
33879
90
32
135
57
27719
100
38
135
57
21559
110
43
135
57
15399
333.6546
222.4364
166.8273
133.4619
111.2182
95.32989
83.41366
74.14547
66.73093
282.323148
188.215432
141.161574
112.929259
94.107716
80.6637566
70.580787
62.7384774
56.4646296
230.9917
153.9944
115.4958
92.39667
76.99722
65.99762
57.74792
51.33148
46.19833
179.6602
119.7735
89.83009
71.86407
59.88673
51.33148
44.91505
39.92449
35.93204
128.3287
85.55247
64.16435
51.33148
42.77623
36.66534
32.08218
28.51749
25.66574
Table 9
We found these values using the equation:
we found the energy required to increase the beverage 25°F from 110°F-135°F to be about 15.4
kJ and when you divide that by time we found the power required. When we used a two minute
time frame, we would need about 128 watts to increase our temperature 25°F.
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Time to Cool Down Beverage
Another important calculation we needed to know was how long we would be able to
keep our beverage at an acceptable temperature before we had to reheat the beverage. In table 10
below, the givens are the mass (m) of the fluid as 0.265 kg, the specific heat ( ) as 4184
J/kg*degK and the resistances (R) found in a previous calculation is shown here to be 9 K/m. To
find the time for the fluid to decrease from 135°F to 115°F with an ambient temperature of 70°F,
we used the following equation:
Givens
mass of fluid
specific Heat
Twater
Tambient
Total Resistance
Tw 1
Tw 2
0.265
4184
330
294
9
330
319
kg
J/kg*degK
K
K
K/m
K
K
time to cool off
2953
49
seconds
minutes
135 deg F
115 deg F
Table 10
We found that it would take 2953 seconds or about 49 minutes for the fluid to decrease
20°F. We found this to be an acceptable time frame because we didn’t want the user to have to
crank up their cup every couple of minutes just to keep their beverage hot. We believed that our
insulation would be sufficient enough to keep the coffee warm for a significant amount of time.
In the thermal testing portion of this report, it is proven that we can keep the fluid warm for the
time we estimated.
Thermal Testing
In order to be able to choose our motor and gearing system, we wanted to perform a
variety of thermal tests to see what power input to the heater we would need to get up to the
desired temperature of 135°F.
We obtained a heater from the company EGC in Chardon. They were gracious enough to
give us a graphite resistive heater for our prototype and testing. They helped us to understanding
the heaters, a test setup and other aspects of the project. Below in figure 12 is a picture of a
similar graphite resistive heater.
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Figure 12
Our first thermal testing procedure was only performed on the inside cup as base testing
and was as follows:
Thermal Testing Validation-Test #1 (Power Validation) Procedure
1. Turn on Power supply and start at 0 Volts/ 0 Amps
2. Apply small amount of electricity to test the heater and to roll out any existing air bubbles
present in between the heater and cup.
3. Measure out 16 oz of water and fill test cup
4. Insert thermometer to determine a baseline temperature for water.
a. Wait until temperature reaches Steady-State
5. Apply a Watt-Density of 1.0 Watts/inches^2 to the heater
6. Record every 20 seconds for 2 minutes
a. Surface Temperature of heater
b. Water Temperature
7. Repeat step 6 for the following Watt-Densities.
a. 1.5 Watt/inched^2
b. 2.0 Watts/inches^2
c. 2.5 Watts/inches^2
d. 3.0 Watts/inches^2
e. 3.5 Watts/inches^2
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1.5Watts/in^2 (delta=5.4deg)
85
Varying Watt Densities
2.0 Watt/in^2 (delta=8.4deg)
80
2.5 Watt/in^2 (delta=10.4deg)
3.0 Watt/in^2 (delta=11.2deg)
3.5 Watt/in^2 (delta=14.95deg)
75
70
65
60
120
100
80
60
Time, Seconds
40
20
0
Figure 13
From figure 13 above, it is shown that using a watt-density of 1.0 W/in^2 we obtained a
delta temperature of 3.5°F. Increasing the watt-density to 1.5 W/in^2 we were able to increase
our delta temperature to 5.4°F and with a watt-density of 2.0 W/in^2 we achieved a temperature
difference of 8.4°F. With a watt-density of 2.5 W/in^2 we recorded a temperature difference of
10.4°F and with 3.0 W/in^2, we increased again to an average temperature difference of 11.2°F.
Our last test at a watt-density of 3.5 W/in^2, we obtained an average temperature of 14.95°F. We
concluded from this test that as we increased the watt-density, we were able to achieve a higher
temperature delta during the two minutes of testing.
Some of our thoughts after the test were that there we noticed a temperature gradient in
the y-direction, where we observed the temperature at the top of the cup was higher than the
bottom. Our inside cup is made of stainless steel and the cup was sitting on a cold plate that
could have caused the temperature difference. We came to the conclusion from this testing that a
3.0 Watt/Inch^2 seemed to be an achievable and consistent watt-density to obtain about a 10°F
temperature difference in a two minute cycle. We also would like to keep the surface temperature
from getting too hot. In our tests we noticed that the surface temperature reached 180°F fairly
quickly and we would like to put a cap on the maximum surface temperature to prevent people
from getting burned.
For our next thermal testing, we wanted to have two thermocouples for the top and
bottom of the mug to better see the temperature gradient in the fluid. We will also do our next
testing with the insulation around the cup and include the lid to cover the fluid.
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Temperature, Deg F
1.0 Watt/in^2 (delta=3.5deg)
The next thermal testing was very similar to the last, but we wanted to see if we did
multiple two minute cycles at a set watt-density to see how much the temperature would increase
over time.
Thermal Testing Validation-Test #2 (Power Validation) Procedure
1. Turn on Power supply and start at 0 Volts/ 0 Amps
2. Apply small amount of electricity to test the heater and to roll out any existing air bubbles
present in between the heater and cup.
3. Measure out 16 oz of water and fill test cup
4. Insert two thermocouples (one for the bottom of the cup and one for the top) to determine
a baseline temperature for water.
a. Wait until temperature reaches Steady-State
5. Apply a Watt-Density of 3.0 Watts/inches^2 to the heater
6. Record every 20 seconds for 2 minutes
a. Surface Temperature of heater
b. 2 Water Temperatures
7. Repeat steps 5 and 6 for 5 cycles.
8. Repeat steps 5 through 7 with the following criteria:
a. With insulation surrounding the cup
b. With the insulation and the lid
Multiple 2 Minute Heating Cycles
140
130
Temperature
120
110
Cup Only (delta=55.6deg)
100
With Insulation (delta=56.6deg)
90
With Insulation and Lid (delta=59.1deg)
80
70
0
1
2
3
4
5
6
7
8
9
10
Time (minutes)
Figure 14
Our results from this experiment displayed in figure 14, showed that we could
continuously increase our temperature by about 11°F during every two minute cycle, but we
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believed by adding the insulation and the lid, we could increase temperature faster and have
more of a temperature delta in the two minute heating cycles. Although it did show some signs of
increasing, we found that by adding the insulation and lid that there wasn’t as much of a
significant change as we thought there would be. By adding just the insulation we gained a 1°F
increase and by adding both the lid and the insulation we gained about 3.5°F.
We also did cool down tests to see how long it would take for our cup to cool down from
135°-100° so that we would know how often we would have to reheat the hot beverage. We
started off with a base test of just the inside liner to see how long it would take to cool down and
in the next test we used insulation to see how much time we could buy. The next test was with
both the insulation and the lid.
Cool Down Testing Validation-Test #1 Procedure
1. Measure out 16 oz of water in a microwavable safe container.
2. Heat water in a microwave about a minute to get the water to a temperature of 135°F and
pour the water into the inside liner of the coffee mug.
3. If the temperature was more than 135°F, the water needs to cool down until it reached
135°F. Use two thermocouples to find the temperature in the water (one towards the top
of the cup and one towards the bottom of the cup).
4. When the water temperature reached 135°F, start the stopwatch and record the
temperature every minute until it reaches 100°F.
5. Repeat steps 1-4, using insulation surrounding the cup.
6. Repeat steps 1-4 again, using the insulation and the lid.
Our results are shown in figure 15 below. In our first test, where we used only the inside
cup liner, it took about 50 minutes for the water to decrease from 135°F to 100°F. In our second
test, with the insulation surrounding the inside liner, the time it took to decrease 35°F increased
to about 70 minutes. In our last test, with both the insulation surrounding the inside liner and the
lid covering the top of the cup, we increase the time it took to decrease 35°F to about 115
minutes.
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Water Temperature, °F
Cooldown Testing Summary
140
135
130
125
120
115
110
105
100
Cup Only
Cup with Insulation, No Lid
Cup with Insulation and Lid
0.00
20.00
40.00
60.00
80.00
100.00
120.00
140.00
Time, Minutes
Figure 15
We did some hand calculations to estimate how long we could keep our coffee at an
acceptable temperature before we would need to reheat the coffee. From our hand calculations,
we estimated it would take about 49 minutes for the beverage to decrease from 135°F to 115°F.
From this experiment, we found that with the inside cup alone it would take about 25 minutes to
decrease to 115°F. With the inside cup and insulation, we found it would take about 32 minutes
to decrease to 115°F. Lastly we found with both the insulation and lid to decrease to 115°F it
would take about 55 minutes, which is longer than what we estimated and we have not tested
with the outside liner. So we expected the time to increase even more with the extra layer around
the cup.
Motor Testing
As stated previously, we wanted a small motor that could give us about 120 Watts with a
low rpm rating because we were using human power and a gearing system to turn the motor.
These motors were only available for expensive prices, and for our prototype we wanted to prove
that our idea worked and eventually we would be able to design our own small motor that could
be mass produced for less money. We were able to obtain a motor that gave us enough wattage,
but its size was much larger than we had hoped. Below in figure 16, is a picture of the motor we
obtained for our original prototype.
23
Figure 16
This motor was rated at producing 250 Watts and 24 Volts, with a revolutions per minute
rating of 2500 rpm. Since we needed only about half the output power the motor was rated for,
we believed if we spun the motor at about half the rpms (1250 rpm), we could obtain slightly
more than the 120 Watts that we needed to heat our beverage. This motor was much bigger than
we were hoping for, as its overall length is 4.0 inches, the overall width is 3.5 inches and the
height is 3.0 inches. With obtaining a larger motor than we expected and wanted, we knew that
our final idea would be to design our own motor that is smaller with our other specifications, but
we wanted to be able to prove out our idea with as little cost as possible.
We did multiple tests on our motor to see if we could produce the desired power and to
also see how easily our motor would increase the temperature of the water. First we started with
a no load test on the motor to measure the maximum voltage that we could input. When finding
the input voltages, we found what rpm rating the motor needed to be running at to achieve the
desired power.
No Load Testing (measure maximum voltage) Procedure:
1. Attach electric drill to the input shaft of the motor.
2. Connect and Calibrate optical tachometer to measure RPM of the shaft.
3. Attach leads of the motor to a multimeter to measure both current and voltage input.
4. Provide 24v to the motor and measure output speed and input current.
5. Continue to decrease the voltage at a rate determined to be reasonable.
24
Zero Load Testing
4000
Motor Input Speed (RPM)
3500
y = 143.55x + 153.02
R² = 0.9891
3000
2500
2000
1500
1000
500
0
0
5
10
15
20
25
Input Power (Watts)
Figure 17
Shown in figure 17 above, as the motor speed in rpm increases, the input power of the
motor increases pretty linearly with a slope of 143.55. Each time the input power is increases by
1 watt the motor speed increases by 143.55 rpms. We noticed we had to spin the motor at higher
speeds to be able to increase the power.
Our next test was to find the output current that we could obtain by spinning the motor
at different speeds.
Maximum Current Test Procedure:
1. Attach electric drill to the input shaft of the motor.
2. Connect and Calibrate optical tachometer to measure RPM of the shaft.
3. Attach leads of the motor to a multimeter to measure both current and voltage input.
4. Spin the motor at roughly 50 rpm and measure the output current.
5. Continue to increase the rpm at a rate determined to be reasonable.
25
Maximum Current Testing
14
Motor Output Current (Amps)
12
y = 0.0177x - 0.5782
R² = 0.9929
10
8
6
4
2
0
0
100
200
300
400
500
600
700
800
Motor Input Speed (RPM)
Figure 18
In figure 18 above, we found the same conclusion that the higher the input speed of the
motor the higher the output current we could obtain. For each 1 rpm increase in the motor’s
speed, the output current would increase by 0.0177 amps. Our last test was done at just over 700
rpms and we could only obtain 12.4 amps.
Our last test with the motor was to attach it to our heater and see how productive it
could be at increasing the temperature of our 16 ounce beverage. This would test if we have a
motor that could adequately do the job that we wanted.
Heater Power Production Benchmarking Procedure:
1. Attach electric drill to the input shaft of the motor.
2. Connect and Calibrate optical tachometer to measure RPM of the shaft.
3. Attach leads of the motor to a multimeter to measure both current and voltage input.
4. Connect leads of the motor to the heater.
5. Install thermocouple inside the mug with 16 oz of water (at ½ depth).
6. Place insulation and lid on the mug.
7. Hook two multimeters into the circuit to measure voltage and current.
8. Record the initial temperature of the water.
9. Spin the motor at a starting RPM of 100 for 1 min.
10. Record the voltage and current 30sec into the test.
11. Record the water temperature at the end of the 1 min.
12. Repeat this test with inreasing rpm’s until the water temperature increases about 10°F.
26
Heater Power Production
Motor Speed
(RPM)
Output
Current
(Amps)
Output
Voltage
(volts)
Delta T (F)
Initial
Final
Output Power
(watts)
805
0.36
5.54
0
67.1
67.1
1.9944
2217
1
15.34
0
67.1
67.1
15.34
Water Temperature (F)
Table 11
From this experiment we were able to find that this motor was not satisfactory with our
heater. In table 11 above it is shown that we increased the speed of the motor quite significantly
but still noticed that there was no temperature change. We also measured our output power from
the motor and found that at the maximum speed we tried of 2217 rpm, we could only obtain
15.34 watts in power. This number is far lower than the 120 watts that we needed to heat our
beverage. From speaking with an employee of EGC company in Chardon where we obtained our
heater, we found that we could design a heater with a watt density of 3.0 watt/in^2 and be
specified to run at 15 volts, which was the maximum voltage we reached with our current motor.
Gearing System
We purchased a preliminary gearing box to gain knowledge and to possibly use in our
design. Below in figure 19, a picture of the gearbox assembly is shown.
Figure 19
This gearbox assembly has a 400 to 1 gearing ratio, which would allow us to have
minimal input to the system, but still be able to spin the motor a significant amount. An example
27
of inputing 12.5 revolutions would give us 5000 revolutions to the motor in a short amount of
time. Although we realize this gearing system would be hard to use with the current motor we
have because the torque required to turn the motor is higher than what a user could easily input
with this 400 to 1 gearing ratio. With such a high ratio, the torque of the input user would have to
be significantly higher than that of a smaller gearing ratio. This is yet to be determined as the
gearbox has not been able to be tested with the motor.
Concluding Remarks
This project has come a long way from staring with magnetic induction to heat our
beverage to now with our theory being proven that we can keep a beverage at drinking
temperature for almost an hour with just our insulation alone. Now we know that we want to
obtain a watt density of 3.0 watt/in^2 and from our motor testing we want a heater that is rated
for about 15 volts. We were able to obtain the 15 volts when we applied a speed of about 2200
rpm’s to the motor. The project is not at a finished state and we still have work to be done. We
currently are waiting on a new heater that covers a diameter of 2.75 inches and a height of 5
inches. The heater will be rated at 3.0 watt/in^2 watt density and be able to operate with an input
of 15 volts. From there, we will be able to interchange our large motor for a smaller one that can
still produce 15 volts with inputting close to the 2200 rpm’s that we had previously found. With
the new motor, we will drop the overall weight and size of the travel mug and be able to make it
one whole entity. With being able to find a new motor, we will be able to design a gearing
system that won’t required a high torque by the user but still be able to obtain the rpm’s needed
operate our motor.
28
Works Cited
Ashby, M. F. (2011). Materials Selection in Mechanical Design. Elsevier Ltd.
FDA Food Code 2009: Annex 3 - Public Health Reasons / Administrative Guidelines - Chapter
4, Equipment, Utensils, and Linens. (2009). Retrieved from FDA US Food and Drug
Administration:
http://www.fda.gov/Food/FoodSafety/RetailFoodProtection/FoodCode/FoodCode2009/ucm1892
12.htm
Thernal Conductivity of Some Commom Materials. (n.d.). Retrieved from The Engineering
Toolbox: http://www.engineeringtoolbox.com/thermal-conductivity-d_429.html
29
Rachel Weyand
Honors Senior Project:
Magnetic Induction Travel Mug
This Project involves a feasibility study and possible design and construction of a travel
mug that is kept warm by the use of magnetic induction. The team is comprised of three
members, Andrew Benner, Eric Yusko, and me, Rachel Weyand. The four areas of focus for this
project are to be heat transfer, electrical circuit, sealing material, and extras.
The heat transfer and the ability of this mug to keep coffee warm will be investigated in
depth. The first step of this is to investigate other coffee mugs and determine what an
acceptable time period will be that we could keep the liquid in our mug hot. This analysis will
also involve the investigation of the “k” value of many possible insulating materials and possibly
a ceramic coating.
The investigation into the electrical circuit will involve many different focuses including
the magnet material, resistors, and capacitors. The first step to this is to look into the existing
magnetic induction flash lights and the power that they produce. From here we can look into
how we can incorporate this technology into a travel mug that will keep a beverage at a desired
temperature for an extended period of time. The magnetic induction system can be evaluated
to see if it is possible to increase the power output and efficiency of the system while still
maintaining a reasonable production cost.
The travel mug will need to have a very unique sealing system so that when the cup is
shaken, to charge the capacitors, its contents will not spill. Different sealing techniques will be
looked at as well as their compatibility with high temperatures.
The final step to the project will be to investigate the cosmetic and extra features that
can be added to this mug. The overall goal of this project is to create a marketable cost
effective travel mug that offers the customer the ability to keep their beverage at desired
temperatures for a long period of time. Some extra features that will be looked at will be an
LCD readout that displays beverage temperature and a led that informs the user when the
coffee mug needs shaken.
We will be working together in most parts of this project, but I alone will be inquiring
the materials study of this experiment. I will be researching the feasibility of different types of
materials throughout the project, whether it will be dealing with sealing or the electrical circuit,
and more specifically, the types of magnets, coiled wires, resistors, and capacitors. An
investigation on prices, sizes, and what temperatures the materials can withstand will be very
important to finding a cost effective product that can be marketable.
30
Eric Yusko, Andy Benner, Rachel Weyand
Senior Design Project: Semester Status Update
December 3, 2010
Design of a Self Heating Travel Mug
The purpose of this paper is to conclude the work that has been done on the senior design
project, which was to design a travel mug that would be capable of maintaining a heated
beverage by means of insulation and an internal heating mechanism. This report documents
fifteen weeks of work that has been done on this project as well as the next steps that will be
needed in order to complete the design of this project.
The first step for designing a travel mug was to set up a plan for the design as well as the
timeline for things that needed to be accomplished. On the next page there is an attached bubble
sheet where the ideas for the travel mug were documented which was used to generate a timeline
for the project. The last page of the report shows a Gantt chart that was created for this project in
order to provide a timeline which provided a structure to the project for completion. The basic
idea behind the travel mug was that there would be an internal electricity generator which would
be used to power a coil heater that would provide heat to the fluid in order to raise/maintain the
temperature of the fluid inside the mug. In parallel, the mug would be insulated in order to
reduce the amount of energy that would be needed in order to accomplish the desired results.
Before things were designed there were certain aspects that needed to be determined. One
of the first things that needed to be determined was the range for acceptable coffee temperature.
Research found that McDonald’s was sued for coffee temperatures that exceeded 160°F. It was
determined for this project that acceptable coffee temperatures were going to range from 100°F
to 140°F. From this information known it was needed to determine how much energy was going
to be needed to heat up water for a certain range of temperatures. The following table shows the
cup and water information used in the calculations:
Volume
Density
mass
Specific
Heat
16
561
2.65E-01
4184
ounces
kg/m^3
kg
J/kgdegC
The next table shows calculations that were performed to show how much energy was required.
These calculations were based on the information from the table above.
31
Initial Temperature ( F)
Initial Temperature ( C)
Final Temperature ( F)
Final Temperature ( C)
70
21
150
66
80
27
150
66
90
32
150
66
100
38
150
66
110
43
150
66
Needed Energy (KJ)
49
43
37
31
25
With this information known, the needed energy was put over time in order to determine
how much power would be needed. This was done since typically electrical devices are labeled
by power rather than energy.
Time in Minutes
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Power(Watts)
412
275
206
165
137
118
103
92
82
75
69
63
59
55
360
240
180
144
120
103
90
80
72
65
60
55
51
48
308
206
154
123
103
88
77
69
62
56
51
47
44
41
257
171
129
103
86
73
64
57
51
47
43
40
37
34
206
137
103
82
69
59
51
46
41
37
34
32
29
27
Once this information was known, the next step was to determine the correct power
source that would be able to generate this type of energy in the most effective and space efficient
way.
The original idea behind the internal heating mechanism was to leverage the technology
from the battery free flashlight. This technology uses magnetic induction to provide electricity
which is stored in a capacitor and used for lighting a LED light. The way that this technology
was going to be levered was by creating a spring and mass system where the shaking input of the
mug would resonate the magnet and spring at its natural frequency creating the maximum
velocity of the magnet passing through an open coil. After reviewing preliminary ideas with
professors in the Electrical Engineering department, it was determined that this type of electricity
generation is really inefficient and was not a practical solution to generating electricity the
internal heating mechanism. The internal heating mechanism took a few different design paths,
but was finally decided it was more practical and efficient to operate a mini electrical motor in
32
the bottom of the travel mug. What was found was by turning an electric motor it would generate
electricity. The next step to conquer was to decide how the motor was going to be spun to create
electricity.
The electric motor can be placed at the bottom of the travel mug where it will generate
electricity to provide energy to the coiled heater which will heat the travel mug. Since the motor
needs to be spun it was decided that the bottom of the travel mug would be free to spin and must
be cranked in order to spin the motor. It was also decided that the way to get the maximum speed
and most work out of the electric motor was to use a gearing system to increase the speed of the
motor. Along with a gearing system a torsion spring will be used in order to store the energy
from the hand cranking.
33
Appendix C
Thermal Testing Validation-Test #1 (Power Validation)
theoretical
Watt
Density
Power
Voltage
Current
Resistance
Area
Initial
Temps
Time
(seconds)
100
80
60
40
20
0
1.0
40.0
24.5
1.63
15.0
40.0
0.956
38.22
24.5
1.56
15.0
40.0
75.6
74.5
81
82.9
83.1
83.7
84.9
85.8
Watt
Density
Power
Voltage
Current
Resistance
Area
Initial
Temps
100
80
60
40
20
0
theoretical
Watts/in^
2
Watts
Volts
Amps
ohms
inches^2
Heater
Fluid
Surface
Temperature
Temperature
(F°)
(F°)
74.5
74.7
75
75.6
76.6
78
delta
Time
(seconds)
actual
2.13
85.284
37.08
2.30
15.0
40.0
70.9
69.6
Heater
Fluid
Surface
Temperature
Temperature
(F°)
(F°)
delta
1.61
64.2
32.1
2.00
15.0
40.0
76.5
76.1
Time
(seconds)
Heater
Surface
Temperature
(F°)
Fluid
Temperature
(F°)
100
80
60
40
20
0
91
92.1
93.2
93.9
95
95.9
75.9
76.1
76.8
78.3
79.7
81.5
69.8
70.2
71.6
73.6
75.6
78
8.4 degF
delta
Watts/in^
2
Watts
Volts
Amps
ohms
inches^2
actual
1.5
60.0
30.0
2.00
15.0
40.0
3.5 deg F
2.0
80.0
34.6
2.31
15.0
40.0
92.8
95.9
97.7
99.5
100
102
Watt
Density
Power
Voltage
Current
Resistance
Area
Initial
Temps
Watt
Density
Power
Voltage
Current
Resistance
Area
Initial
Temps
5.4 deg F
2.5
100.0
38.7
2.58
15.0
40.0
2.58
103.25
41.3
2.50
15.0
40.0
67
64.6
Time
(seconds)
Heater
Surface
Temperature
(F°)
Fluid
Temperature
(F°)
100
80
60
40
20
0
93.6
96.8
97.5
99.1
101
102
64.8
65.5
67.3
70
72.5
75
delta
10.4 degF
34
theoretical
Watt
Density
Power
Voltage
Current
Resistance
Area
Initial
Temps
Time
(seconds)
100
80
60
40
20
0
actual
3.0
120.0
42.4
2.83
15.0
40.0
3.04
121.52
43.4
2.80
15.0
40.0
68.4
66.6
Heater
Fluid
Surface
Temperature
Temperature
(F°)
(F°)
94.1
97.3
99.1
101
104
106
delta
66.6
67.1
69.3
72
74.8
77.7
11.1 degF
theoretical
Watts/in^2
Watts
Volts
Amps
ohms
inches^2
Watt
Density
Power
Voltage
Current
Resistance
Area
actual
3.5
140.0
45.8
3.06
15.0
40.0
3.44
137.7
45.9
3.00
15.0
40.0
Time
(seconds)
Heater
Surface
Temperature
(F°)
Fluid
Temperature
(F°)
120
100
80
60
40
20
0
68.5
102
106
108
111
114
116
64.2
64.4
65.2
68
71.6
75.2
79
delta
14.8 degF
35
Thermal Testing Validation-Test #2 (Power Validation)
Cup Only
theoretical
Watt
Density
Power
Voltage
Current
Resistanc
e
Area
3.0
120.0
42.4
2.83
actual
3.085
123.384
42.4
2.91
15.0
40.0
Watts/in^2
Watts
Volts
Amps
7
2
.
1 degF
Tambient
15.0 ohms
40.0 inches^2
Heat Cycle #1
Heat Cycle #2
Heat Cycle #3
Heat Cycle #4
Time
(seconds)
Fluid
Temperat
ure (F°)
Top
Fluid
Temperat
ure (F°)
Bottom
Fluid
Temperatu
re (F°) Top
Fluid
Temperat
ure (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Temperat
ure (F°)
Bottom
120
100
80
60
40
20
0
76.5
75.4
76.1
78.4
81.9
85.3
88.9
76.3
76.6
76.6
76.8
76.1
76.5
77
93.2
93.9
95
97.3
99.9
102.6
105.1
79.3
79.7
84
81.9
83.3
85.1
86.5
108
108.5
110.3
112.3
115.7
118
120.4
88.7
89.1
90.1
91.6
93.2
94.8
96.6
122.2
122.5
124.3
126.1
128.3
130.1
132.1
98.8
99.1
101.3
102.4
104.5
106
107.6
12.4
0.7
11.9
7.2
12.4
7.9
9.9
8.8
Delta
36
With Insulation
Heat Cycle #1
Heat Cycle #2
Heat Cycle #3
Heat Cycle #4
Time
(secon
ds)
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
120
100
80
60
40
20
0
73.9
73.9
74.3
76.3
79.3
82.4
85.6
74.5
74.5
74.5
74.5
74.7
75.2
75.9
89.2
90
92.6
93.9
96.6
99.3
101.8
78.1
78.4
79.3
80.6
82.2
84.2
85.8
105.3
105.8
107.4
109.6
111.9
114.4
116.8
88
88.3
89.4
91
92.7
94.5
96.3
119.7
120.2
122.2
124.2
126.3
128.5
130.5
98.4
98.8
100.2
102
104
105.8
107.4
Delta
11.7
1.4
12.6
7.7
11.5
8.3
10.8
9
With Insulation
and Lid
Heat Cycle #1
Heat Cycle #2
Heat Cycle #3
Heat Cycle #4
Time
(secon
ds)
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
Fluid
Tempera
ture (F°)
Top
Fluid
Tempera
ture (F°)
Bottom
120
100
80
60
40
20
0
74.1
74.1
74.5
76.5
79.7
82.9
86.2
74.7
74.5
74.5
74.5
74.5
74.8
75.4
89.6
90.3
92.1
94.5
97
99.7
102.6
76.8
77.2
77.7
78.6
79.9
81.3
82.8
105.6
106.2
108.1
110.3
112.6
115.2
117.9
84.9
85.5
86.5
87.8
89.1
90.5
91.9
121.5
122
123.8
126.1
128.3
130.6
133.2
94.3
94.8
96.1
97.7
99.3
101.3
103.3
Delta
12.1
0.7
13
6
12.3
7
11.7
9
37
Cool Down Testing
Test 1: No Insulation/Lid
Bottom
Time
Top Tc
Tc Deg
min:sec
Deg F
F
0.00
135
135
5.00
129.6
129.6
10.00
125.1
125.1
15.00
121.1
120.9
20.00
117.1
117
25.00
113.7
113.7
30.00
110.7
110.7
35.00
108
108
40.00
105.6
105.6
45.00
103.5
103.5
50.00
101.3
101.1
Test 2: Insulation, No Lid
Bottom
Time
Top Tc
Tc Deg
min:sec
Deg F
F
0.00
135
135.4
5.00
131.2
131.5
10.00
127.6
127.9
15.00
124.5
124.9
20.00
121.5
121.8
25.00
118.4
118.9
30.00
115.7
116.2
35.00
113.2
113.7
40.00
110.8
111.4
45.00
108.9
109.4
50.00
107.1
107.4
55.00
105.4
105.8
60.00
103.8
104.4
65.00
102
102.6
70.00
100.2
100.9
Delta
Temp
0
1.6
2.5
3.4
4.4
4.7
5
5.2
5.2
5.4
5.8
Test 3: Insulation, Lid
Bottom
Time
Top Tc
Tc Deg
min:sec
Deg F
F
0.00
135
135.5
5.00
132.8
132.4
10.00
130.6
130.3
15.00
128.7
128.1
20.00
126.9
126.3
25.00
124.9
124.3
30.00
123.3
122.7
35.00
121.5
120.9
40.00
119.7
118.9
45.00
117.9
117.3
50.00
116.2
115.7
55.00
114.8
114.1
60.00
113.2
112.6
65.00
111.7
111.4
70.00
110.5
109.9
75.00
109.2
108.9
80.00
108.1
107.6
85.00
106.9
106.5
90.00
105.8
105.4
95.00
104.9
104.5
100.00
103.8
103.5
105.00
102.7
102.4
110.00
101.7
101.3
115.00
100.6
100.3
38
Appendix D Raw Data for Motor Testing
No Load Test (zero current)
Motor Speed (RPM)
3250
2985
2701
2419
2140
2008
1870
1732
1595
1455
1218
1184
1047
911.1
757.7
638.2
201.8
367.2
230.3
95.6
Input Current (Amps)
0.94
0.92
0.9
0.87
0.84
0.84
0.83
0.81
0.79
0.77
0.75
0.73
0.7
0.67
0.64
0.61
0.58
0.55
0.52
0.49
Input Voltage (volts)
24
22
20
18
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Input Power (watts)
22.56
20.24
18
15.66
13.44
12.6
11.62
10.53
9.48
8.47
7.5
6.57
5.6
4.69
3.84
3.05
2.32
1.65
1.04
0.49
Maximum Current Test (zero Voltage)
Motor Speed (RPM)
713.4
572.9
537.6
474
419
357
302
258
236
201
166
139
105
66
Output Current (Amps)
12.4
10
8.6
7.6
6.6
5.6
4.6
3.95
3.05
3
2.5
2
1.4
1
39