Propane Tank Math

Posted on 1-January-2016 by mathscinotes

Quote of the Day

The Martian is the best advert for a career in engineering I've ever seen.

- Brian Cox (physicist), tweeted this review of 'The Martian' movie.

Introduction

Figure 1: Propane Heater I Just Purchased.

Figure 1: Propane Heater I Just Purchased (Source).

I have some woodworking I need to do, and my little woodshop is in my garage. Unfortunately, Minnesota is quite cold at the moment, and working in the garage is not comfortable. After decades of working out in the cold, I decided it is time to get a small heater to make things a bit more comfortable.

I have used propane for years with my barbecue grill, but I have never used it for heating a space. I know that there is an Ashland propane delivery provider for people who heat their space this way, but here I just went and got one when I was out. While at university many decades ago, I worked in construction, and we used propane heaters to make working in partially completed homes more comfortable in the winter. I went to Home Depot and purchased the propane heater shown in Figure 1. It is rated to put out 30K to 40K BTU/hr. This should provide enough heat to warm my garage so I can work in it comfortably. I like the fact that it is small, and I can easily store it during the summer. I have too much stuff to manage as it is, and I do not need any more big stuff.

Background

Definitions

Tare Weight (TW)
Tare weight, sometimes called unladen weight, is the weight of an empty vehicle or container (Source).
Commercial Propane
This product consists of a hydrocarbon mixture containing predominantly propane (Source).
Water Capacity (WC)
The water capacity is how much water the propane tank will hold in pounds. For example, the "WC" stamped on the tank followed by a number such as "47.6" means the tank will hold 47.6 pounds of water. (Source).

Tank Construction

Figure 2 shows the internal construction of a typical 20 lb propane tank.

Figure 2: Propane Tank Construction.

Figure 2: Propane Tank Construction (Source).

Appendix B provides some information on the how the pressure in a propane tank varies with temperature.

Analysis

Volume of Propane in a 20 lb Cylinder

My old propane tank is shown in Figure 3. It has a WC=47.6 lbs and TW=18 lbs.

Figure M: Rating on My Propane Tank.

Figure 3: Rating on My Propane Tank.

I can compute the weight and volume of propane in this tank as shown in Figure 4.

Figure M: Demonstration of Way a 20 lb Tank is Named Such.

Figure 4: Demonstration of Why a 20 lb Tank is Named Such.

20% Safety Margin

I found the following statement in this document.

A tank filled with a volume of 80% liquid phase at 0 C will be full at a temperature of 60 C. At the same time, the density of propane in the liquid phase decreases from 530 to 430g/l.

Requiring 20% of margin reserve allows the propane to expand when the temperature rises. Figure 5 shows how I confirmed this statement using the propane density versus temperature relationship I compute in Appendix A – I thought it was a bit messy to include in the main post.

Figure M: Verification of 60 C Temperature Rise Filling a Tank.

Figure 5: Verification of 60 C Temperature Rise Filling a Tank.

In Figure 5, I derive a rate of 1.9% volume expansion for every 10 F of temperature rise, which assumes a constant mass. The Wikipedia lists 1.5% volume expansion for every 10 F. My value is in the ballpark, but not as close as I like to be.

Operating Time At Maximum BTU Generation Rate

Figure 6 shows my estimate for the amount of heating time I should expect from a 20 lb tank of propane – 10.8 hours. The energy density of propane comes from this source.

Figure M: Estimate Run Time Calculation.

Figure 6: Estimate Run Time Calculation.

The 10.8 hour value is also quoted in the heater manual (Figure 7).

Figure 4: Heater Manual Run Time Specification.

Figure 7: Heater Manual Run Time Specification.

Conclusion

I like to understand a bit about any product I use. This analysis gave me a bit of insight into how propane is used for space heating.

Appendix A: Liquid Expansion Model

Since I wanted to understand how propane expands with temperature, I need some information. I found this excerpt on the web that provide a functional model based on curve-fitting data.

Eq. 1 \displaystyle \rho =A\cdot {{B}^{{-\left( {1-\frac{T}{{{{T}_{C}}}}} \right)\cdot n}}}

where

  • A, B, n, TC are curve-fit generated parameters.
  • T is the temperature in Kelvin.

Unfortunately, I was not able to find parameters for propane (C3H8). So I decided to put together my own model. The model of Equation 1 is a bit difficult to fit because it has some parameters that are not independent. For my work here, I will use the model shown in Equation 2.

Eq. 2 \displaystyle \rho (T)=\alpha\cdot {{\beta}^{{\gamma\cdot T}}}

where

  • α, β, and γ are curve-fit generated parameters.

I searched the web and found some density data points for commercial propane, which is not pure propane because it also contains other fuels like butane and methane. Figure 8 show the results of my curve-fitting exercise.

Figure M: My Curve-Fitting of Propane Density Data.

Figure 8: My Curve-Fitting of Propane Density Data.

Figure 9 graphically shows the quality of the curve-fit to the data. Note that in this limited temperature region, a linear model would have sufficed.

Figure M: Curve-Fit Vs. Raw Data.

Figure 9 Curve-Fit Vs. Raw Data.

Appendix B: Tank Pressure Vs. Temperature

Figure 10 shows how the tank pressure varies with temperature.

Figure M: Tank Presure Versus Temperature.

Figure 10: Tank Pressure Versus Temperature (Source).

Posted in General Mathematics | 5 Comments

Shoot Boards for Handheld and Table Saws

Posted on 31-December-2015 by mathscinotes

Quote of the Day

The difficulty lies not so much in developing new ideas as in escaping from old ones.

— John Maynard Keynes

Introduction

Figure 1: How I Would Love to Have A Full-Size Table Saw.

Figure 1: How I Would Love to Have A Full-Size
Table Saw (Source).

I live in a small home, and I have to do my woodworking in the garage. Since I have two cars that "live" in the garage, I do not have sufficient room for a full-size table saw (Figure 1).

The biggest challenges I face have to do with cutting large sheets of plywood (4' x 8'). Without the space for a table saw, I had to begin looking for alternative approaches that I could setup and teardown in my garage.

Shoot Boards For Circular Saws

Figure 2: Standard Shootboard.

Figure 2: Standard Shoot board (Source).

When I began woodworking, I cut my plywood to size using a circular saw and a shoot board that looks identical to that shown in Figure 2 (detailed plans here).

This approach served me well for many years, and I have a number of furniture pieces that were done with this simple, yet effective, saw guide. The main issue with this approach has to do with the jagged cut left on the top-side of saw cut, which is called tear-out (Figure 3). Admittedly, the shoot board does greatly reduce tearout, but I still get some.

There are ways to minimize the tear-out using masking tape and cutting with the finish side down (discussed here), but these are less than ideal solutions because you really want a clean cut on both sides of your workpiece.

The solution to the problem of tearout is the use of a zero-clearance base for the circular saw. You can see a homemade zero-clearance base in Figure 4. However, using a homemade shoot board and zero-clearance base was a bit of a problem because you do have to occasionally replace the base as you change the saw depth-of-cut, and the edge of edge of the shoot board eventually gets ragged.

Figure 3: Example of Tearout (Source).

Figure 3: Example of Tear-out (Source).

Figure 4: Homemade Zero-Clearance Saw Base.

Figure 4: Homemade Zero-Clearance Saw Base (Source).

For the last five years, the best solution I have found is the EZ Smart Track Saw (Figure 5). This saw has a replaceable saw base and cutting edge so that I always can make straight clean cuts. I highly recommend this system. One quaint aspect of EZ Smart is that when I called them with a question, I ended up talking to the company founder, Dino.

Figure 5: EZ Smart Track Saw Video.

Shoot Board for a Table Saw

When I learn a new technique, I always start to think about how to generalize its application – generalizing is the part of mathematics that I find the most interesting. I was interested in whether there was an equivalent of a shoot board for a table saw? I found the answer to my question in the L-Fence shown in Figure 6. I love the simplicity and safety of this approach. Nice work by the Connecticut Valley School of Woodworking Director Bob Van Dyke.

Figure 6: L- Fence, A Table Saw Equivalent of a Shoot Board.

Figure 6: L- Fence, A Table Saw Equivalent of a Shoot Board (Source).

Since I do have a small, portable table saw for cutting small pieces that the track saw cannot handle safely, I am going to experiment with this fence over the next few weeks. I should mention that Finehomebuilding has an excellent video featuring Bob at this site.

Posted in Construction | Comments Off on Shoot Boards for Handheld and Table Saws

Output Voltage Control Circuit Design

Posted on 30-December-2015 by mathscinotes

Quote of the Day

I am only an average man, but by George, I work harder at it than the average man.

— Theodore Roosevelt. I think about this quote often. I have worked with some very bright people, but the folks who really accomplished things were all hard workers.

Introduction

Figure 1: Questions Were About This Circuit.

Figure 1: Questions Were About This Circuit.

While I am in management, I still get an occasional circuit design question – I really like these questions because the get me away from some of the monotonous aspects of management (i.e. budgeting). This morning a power supply designer stopped by and wanted to discuss an issue he was having with fixing an issue with an old design. I immediately dropped my budgeting activity and leaped into action.

Basically, the old design was working, but the output voltage needed to be made variable to compensate for variations we have observed. Here are his constraints:

  • No major changes to the circuit because we need to use the same test fixture
    • No added parts
    • Minor trace changes are allowed
    • Test points cannot be moved
  • The required output voltage changes required are small
  • We do have a spare Digital-to-Analog (DAC) converter available

While the circuit was quite complex overall, the part involved with setting the output voltage is simple (Figure 1). The solution ended up summing the spare DAC's output voltage with the power supply feedback control signal. The focus of this post is how I determined the correct value of the summing resistors. It was a nice application of Mathcad that I am going to use for a training class that I will be conducting early in 2016.

Analysis

Requirements

The requirements are straightforward:

  • DAC can put out 0.25 V to 2.5 V
  • We need the output voltage to vary from 0.7 V to something higher than 1.1 V.
  • The DAC is tri-state (i.e. high-impedance) on powerup. The circuit must be well-behaved with the DAC output tri-stated.

Modeling

Figure 2 shows my circuit analysis, which determines the resistor ratio (RT/RS) as a function of the minimum output voltage level.

Figure 2: Circuit Analysis.

Figure 2: Circuit Analysis.

Graphical View

Figure 3 shows a graphical presentation on how the output voltage varies with different minimum output voltages.

Figure 3: Output Voltage Variation As a Function of Minimum Output Level.

Figure 3: Output Voltage Variation As a Function of Minimum Output Level.

Component Selection

Figure 4 shows how I selected my components. In this selection, I used a program that I wrote that computes the optimal resistor values for a given ratio.

Figure 4: Computing the Specific Resistor Values.

Figure 4: Computing the Specific Resistor Values.

Conclusion

While this was a routine calculation, it does illustrate the process of optimizing a circuit subject to many constraints.

Postscript

The circuit test was just completed today (4-March-2016) and the circuit passed all tests.

Posted in Electronics | Comments Off on Output Voltage Control Circuit Design

Tidal Timing

Posted on 23-December-2015 by mathscinotes

Quote of the Day

The final test of a leader is that he leaves behind him in other men the conviction and the will to carry on.

— Walter Lippmann. I completely agree with this statement – your legacy as a manager is the team and processes that you formed while you were in charge.

Introduction

Figure 1: Illustration of the Cause of Tides.

Figure 1: Illustration of the Cause of Tides (Source).

After a discussion on the annual time shift of the winter solstice, our lunch time topic changed to the topic of tides. During this discussion, I mentioned that tides have a period of about 12 hours and 25 minutes (Figure 1). I will show you how to compute this period in this post.

The key to understanding this odd period is to note that the Moon creates the tides by pulling on the ocean, which  means the tides follow the motion of the Moon. Because of how gravity and inertia work, there is also a second tidal bulge on the side of the Earth opposite of the Moon. Thus, we experience two tides for each time the Moon passes over our heads.

To compute the period of the tides, we begin by computing the period of the tidal bulge that moves underneath the Moon. Since the Earth is rotating on its axis and the moon is revolving around the Earth, the period of the Moon's orbit as seen from an observer on the Earth is longer than 24 hours because the Earth must "catch up" with the Moon for it to be seen in its same position as the time of the last tide.

I will be working approximately here – it turns out that tides are also a function of the position of the Sun, which I will be ignoring. We can compute the period of the tides using the approach shown in Figure 2. My rough calculations show the tidal period is about 12 hours and 26 minutes.

Figure 2: Calculation of the Period and Tide Period.

Figure 2: Calculation of the Period of Tides.

There are numerous subtleties associated with computing the exact period of the tides. For more details, see this web page and the Wikipedia.

Posted in Astronomy | Comments Off on Tidal Timing

A Little Solstice Math

Posted on 22-December-2015 by mathscinotes

Quote of the Day

The question really isn't whether it's right, the question is can it be useful to people so they can understand the world around them and make better decisions.

— Milton Friedman on conceptual frameworks and theories. The longer I work in the technology field, the more I realize that creating a decision-making framework is a critical, but often overlooked part of problem solving.

Figure 1: Earth-Sun Orientation During Equinoxs and Solstices

Figure 1: Earth-Sun Orientation During Equinoxes and Solstices (Source).

We just went through the winter solstice of 2015, which in Minnesota is a subject of celebration. This means that we will now start to see more daylight.

The time of the winter solstice varies each year. It occurs on either 21-Dec or 22-December. One of the engineers in my group asked how the time of the winter solstice moves year-over-year. My response was that it moves forward ~six hours each year until a leap year happens, which resets the cycle.

A little calculation is often the best teaching example, so I put together the following table. In this table, I have the time of the solstices since 1980 to 2020, and computed the time increment from year-to-year. This table does a decent job of showing that the solstice times do increment by a bit less than six hours each year. I did my calculations assuming UTC. In Minnesota, we would normally use Central Time.

Figure 2: Table of Winter Solstices And Yearly Time-Shifts.

Figure 2: Table of Winter Solstices And Yearly Time-Shifts.

As you can see in Figure 2, the yearly time shift averages 5 hours and 48 minutes. In Figure 2, you can also see that a calendar year has ~365.242 days in it.

 

Posted in Astronomy | 1 Comment

Stairway Rise Angles

Posted on 21-December-2015 by mathscinotes

Quote of the Day

History is a tool used by politicians to justify their intentions.

— Ted Koppel

Figure 1: I Consider A Well-Done Stairway to be Mathematics in Wood.

Figure 1: A Well-Designed Stairway is
Mathematics Carved Wood (Source).

I was reading this month's Journal of Light Construction (JLC) when I saw an article on building safe stairways per the International Residential Code (IRC). I have written about stairway rise angles before, but from the standpoint of three commonly used stairway design rules of thumb. The IRC provides a hard upper limit that is lower than the maximum permitted by the most liberal of these rules of thumb.

The JLC article (which I cannot find online) provides an interesting graphic (Figure 2) that shows a maximum stair angle of 37.78° (red line).

These angles are important because people are quite sensitive to even minor changes in stair rise angles.

Figure 2: JLC Graphic Showing IRC Maximum Angle.

Figure 2: JLC Graphic Showing IRC Maximum Angle.

The IRC sets the maximum allowed stairway rise angle by setting the maximum rise and minimum run. Figure 3 shows how to use these values to calculate the maximum stairway rise angle (green highlight) allowed by the IRC. I have also included the stairway rise angles for some other common rise/run combinations. The vast majority of stairways have rise angles between 30° and 35°.

Figure 3: Angles for Common Stairway Risers and Tread Lengths.

Figure 3: Angles for Common Stairway Risers and Tread Lengths.

I have to admit that I love designing stairs and roofs. There is something magical about using a few formulas to create something that is both beautiful and functional.

Posted in Construction | 2 Comments

Incorrectly Computed Discount Followed By Markup

Posted on 20-December-2015 by mathscinotes

Quote of the Day

Doubt is not a pleasant condition, but certainty is an absurd one.

— Voltaire. I have to agree – it seems that the most dangerous people are often those who are absolutely certain of something, but should not be.

Introduction

Figure 1: Tile Looks Great, But I Do Not Like to Install It.

Figure 1: Tile Looks Great, But I Do Not Like to Install It (Source).

A few years ago, I hired a tile installer to tile a bathroom I was remodeling. He was a talkative guy, and he casually mentioned that he had chosen not to make any money on his material – he would make his money on labor alone. He said that most of the tile shops he works with give him a 15% discount on material, which he passes on to his customers. Other contractors markup their material charge by 15% to bring the cost back to retail price – this statement bothered me because the markup should be larger than the discount. The math did not seem right to me at the time, but I did not raise any questions because I wanted my bathroom done. I did not think much about this math error at the time until I saw an article in the Journal of Light Construction (JLC) telling contractors that this is a math error that is costing them money. As I read the article, I realized that this is exactly the same error I heard my tile contractor make.

I have seen a variation of this error when engineers will use conversion cost (which is really a margin) as a markup (see this post for more information). The key is to understand that a percentage discount on a product's cost does not equal the markup required to bring the discounted product price back to its original value.

Analysis

Example Error

Figure 2 shows the math error that my tile installer would have made if he chose to markup his cost by the supplier's discount percentage. The contractor thought that the cost reduction due to a percentage discount would be cancelled out by a markup of the same percentage – it is not.

Figure 2: Tile Installer Math Error.

Figure 2: Tile Installer Math Error.

Reason For The Error

Figure 3 shows why the error occurs. Essentially, there is an error term equal to the square of the discount rate.

Figure 3: Reason For The Discount/Markup Error.

Figure 3: Reason For The Discount/Markup Error.

Correct Markup Derivation

Figure 4 shows the equation for the markup value (highlighted) that the contractor should have used. Note that computer algebra systems often throw an arbitrary minus sign onto the front of their simplified expressions. I do not know why – however, the expressions they derive are correct.

Figure 4: Derivation of the Correct Markup Percentage.

Figure 4: Derivation of the Correct Markup Percentage.

I summarize this result in Equation 1.

Eq. 1 \displaystyle {{K}_{{Markup}}}=\frac{{{{K}_{{Discount}}}}}{{1-{{K}_{{Discount}}}}}

where

  • KDiscount is the discount from the tile vendor.
  • KMarkup is the markup the tile installer must apply to his tile cost to get back to the retail cost

Correct Markup Example

Figure 5 shows how the markup should have been computed for the tile contractor to get back to the original price.

Figure 5: Example of a Correctly Computed Markup.

Figure 5: Example of a Correctly Computed Markup.

Conclusion

I see people make these percentage calculation errors all time. The most common one I see is to use conversion cost as markup rather than a margin. I will provide a quick example of this error here:

  • Assume I am buying an assembly from a contract manufacturer for $100.
  • Assume the contract manufacturer is charging me 12% of this $100 for his assembly charge, which is called the conversion cost.
  • This means that the material cost (i.e. BOM cost) is $88.
  • Engineers normally know the BOM cost and try to calculate the assembly charge by multiplying $88·12%=$10.56, which is incorrect.
  • The correct way is determine the markup using Equation 1, 12%/(1-12%)=13.6%. Now we can take $88·13.6%=$12, which is the correct answer.

When it comes to calculation errors, none are more common than those that involve dB.  The most common dB calculation error I see is to use 10 log () instead of 20 log() when working with voltage.

Posted in Construction, Financial | Comments Off on Incorrectly Computed Discount Followed By Markup

Building an MST3K Tom Servo Replica

Posted on 19-December-2015 by mathscinotes

Quote of the Day

Price has no meaning without a measure of the quality being purchased.

— W. Edwards Deming. I have had this lesson reinforced many times.

Introduction

Figure 1: MST3K Cast with Tom Servo Highlighted.

Figure 1: MST3K Cast with Tom Servo Highlighted.

I have a great fondness for Mystery Science Theater 3000 (MST3K). As I have mentioned in other posts, I spent many hours with my young sons watching Joel Hodgson, Tom Servo, and Crow watch movies on the Satellite of Love (Figure 1). While it has been off-the-air for many years, there is a move afoot to bring MST3K back on Kickstarter right now.

I do have a favorite character on the show – Tom Servo. I consider him one of the best characters in the history of television. In some respects, he plays a similar role to that of Bender on Futurama, with a dash of Zapp Brannigan.

Apparently, my fondness for Tom Servo is shared by many others, including my son's girlfriend. My son decided to build a Tom Servo replica for her as a Christmas present. He asked me if I could help with the painting – in an earlier time, I did quite a bit of car painting.

Figure 2: Our Completed Tom Servo Replica.

Figure 2: Our Completed Tom
Servo Replica.

In this post, I will provide some photographs I took during our build effort. These photographs do not constitute detailed instructions on how to build the unit, but you will see the general idea.

Our Tom Servo  is working puppet. His head is on a turntable that can be rotated by turning a small PVC pipe in his base. His mouth can be opened and closed by pulling on a wire that we ran from his mouth down into the base.

My son acquired most of the parts for this build from an ebay store ran by Bob Bukoski. The kit had all the hard to find components, and we supplied all the paint, masking tape, etc.

The only thing I would change was our use of Testor spray paint, which was recommended. That paint runs like no paint I have ever sprayed before. I was able to adapt my spray technique, but it was still way too easy to run that paint.

A Few Photographs

Figure 3(a) shows the candy dispenser used to make Tom's head. Figure 3(b) shows the base of the candy dispenser from the kit after  I have removed most of the black handle that is used to open the dispenser's mouth. Only a tiny corner is left.

ffff ffff
Figure 3(a): Carousel Snack Dispenser (Source). Figure 3(b): My Modified Snack  Dispenser.

Figure 4 shows the modification made to Tom's head that allowed us to open his mouth using a wire.

Figure 4: Modification of the Candy Dispenser To Open Its Mouth By Pulling a Wire.

Figure 4: Modification of the Candy Dispenser To Open Its Mouth By Pulling a Wire.

Figure 5 shows the fully assembled and painted head mechanism. The mouth is controlled by a wire that is running through the PVC pipe.

Figure 5: Tom's Head Assembly.

Figure 5: My Son Holding Tom's Head Assembly.

Figure 6 shows a PVC T-coupler that was modified to fit into Tom's head (Source). This is similar to the one that was in the kit – I forgot to take a picture of it, but this one is similar. The modified T-coupler was hot melt glued into Tom's head for the PVC pipe to mount into.

Figure 6: Altered PVC T-Coupler That Mounts in Head.

Figure 6: Altered PVC T-Coupler That Mounts in Head.

Figure 7 shows a side view of the model.

Figure 6: Side View of the Assembled Tom Servo.

Figure 6: Side View of the Assembled Tom Servo.

Conclusion

This was a fun exercise. I hope my son's girlfriend likes her Tom Servo. I am now trying to talk my son into working with me on a Raspberry Pie project.

I will finish this post with the Tom Servo Theme Song.

Posted in Humor | Comments Off on Building an MST3K Tom Servo Replica

Selecting a Thermal Magnetic Circuit Breaker

Posted on 18-December-2015 by mathscinotes

Quote of the Day

Go out and smell like the flock.

— Pope Francis to parish priests, admonishing them to go out and know how people live their lives.

Introduction

Figure 1: Current Rating Multiplication Factor Versus Temperature.

Figure 1: Current Rating Multiplication Factor Versus Temperature (Source).

I have an application that requires a thermal magnetic circuit breaker that will provide a given level of protection at an elevated temperature. Most thermal magnetic circuit breakers have a current rating that is specific to a stated temperature, usually room temperature (~23 °C). In my case, I need a circuit breaker with a 15 A break current at 50 °C.

In the case of E-T-A  breaker shown in Figure 1, the labeled current ratings holds for 23 °C. For other temperatures, a "multiplication factor" is given. For my 50 °C application per Figure 1, I need to specify a breaker with a labeled rating 1.16 times my 15 A requirement or 17.4 A.

This actually makes sense because these breakers sense current by measuring the internally temperature change with a bimetallic strip. This strip is similar to the bimetallic strip in a thermostat. In a circuit breaker, the overload current increases internal temperature of the breaker, which causes the strip to bend and eventually trip the breaker.

If the breaker must function at a temperature higher than its rating, the bimetallic strip bends because of the higher than specified temperature. This would cause the breaker to open at 50°C at a lower current than at 23 °C. Hence, we must compensate for the higher temperature by using a circuit breaker that is rated for more current at room temperature than we need at 50 °C. This is the purpose of Figure 1. The opposite effect occurs if the breaker must function below room temperature.

Here is a useful Youtube video that does a nice job of demonstrating the different operating modes of a thermal magnetic circuit breaker.

Posted in Electronics | Comments Off on Selecting a Thermal Magnetic Circuit Breaker

Those Thrifty German Immigrants ... Combine Repurposed as a Gravedigger

Posted on 17-December-2015 by mathscinotes

Quote of the Day

You fall out of that tree and break both your legs, don't come running home to me.

— My mother on safety. When I see a child today riding a bicycle and wearing a helmet and pads, I wonder how I survived childhood.

Figure 1: Gleaner Combine as Originally Configured.

Figure 1: Gleaner Combine as Originally Configured.

I am the son and grandson of German  farmers. Their farms were almost magical to me because of all the belts and pulleys used to drive everything – it would have been an OSHA nightmare. I was always impressed with the self-sufficiency of these farms. For example, the Biegert farm in Hanover, Minnesota had a small sawmill that was powered using a tractor's PTO. Many farm buildings in that small community were built using wood from local trees cut by that mill. In fact, my family still has an affection for woodworking using butternut because that was a wood our father often milled on the farm. I smile just thinking about it.

Figure 2: Gleaner E Combine Repurposed as Gravedigger.

Figure 2: Gleaner E Combine Repurposed as Gravedigger.

One of the engineers in my group stopped by the other day and wanted to show me a photograph of an obsolete combine harvester that had been repurposed in an unusual way. The small German community of New Munich had removed the combine head and replaced it with a digging tool. It is now used by the local cemetery as a grave digging tool. This is exactly the sort of thing the old German farmers in Hanover would have done.

Posted in History of Science and Technology, Humor | Comments Off on Those Thrifty German Immigrants ... Combine Repurposed as a Gravedigger