# My Little Gilligan's Island - Part 1 (The Shower)

## Introduction

My cabin in northern Minnesota is very primitive (the only water is lake water, no heat, no air conditioning, no phone, no Internet) and I do not want to put any money into it until I get my sons through college. I do have electrical power. To make the cabin more livable, I have developed a few ways to make things a bit more comfortable for little extra money. One thing I have put in is a primitive lake water shower. This blog post goes into how the shower was put together and how we use it. There was a bit of design in resolving this issue and this post describes my solution.

## Design Approach

When my wife and I first bought the cabin, we tried to stay clean by bathing in the lake. Unfortunately, the lake temperature never gets above the mid-70 °F range during the summer, and during spring and fall it drops below 50°F (it freezes over in winter). This makes for very uncomfortable bathing. To make bathing comfortable, my basic approach will be to bring the water up from the lake to a storage area, heat it, and then use it for showering. This approach required me to solve the following problems.

• Transporting the lake water
• Storing the lake water
• Heating the water
• Designing a shower (pump, plumbing, nozzle, shower enclosure)
• Removing the gray water

Let's take these items one by one.

### Transporting the Lake Water Up the Hill

The most convenient place for the shower is about 100 feet from the lake and up a 15 foot hill. Let's think about the amount of water I will be needing for a showering.

• It is not unusual for me to have 8 people at the cabin.
• A typical shower head puts out 3 gallons per minute.
• A typical shower takes about 2 minutes.

The total amount of water required for the showers is given by the following equation.

$V = N \cdot t \cdot F = 8{\text{ showers}} \cdot 2\frac{{\min }}{{{\text{shower}}}} \cdot 3\frac{{{\text{gal}}}}{{{\text{min}}}} = 48{\text{ gal}}$

where V is the total volume of water (gallons), N is the number of people showering (8), F is the flow rate (3 gallons per minute), and t is the length of an average shower (2 minutes). This means that I need 48 gallons of water for showering. Since water weighs ~8 pounds per gallon, I need nearly 400 pounds of water. Using pails to move the water up the hill is not an option. I need a pump. It turns out that I actually designed a pump system that works well. I will discuss the pump system in a later blog post. Assume for now that I am using an electrical pump to bring the nearly 400 pounds of water up from the lake to a storage area. My pump average 15 gallons per minute, which is about 120 pounds of water per minute. This means that I can move all the water I need in less than 4 minutes with no lifting.

### Storing the Lake Water

The cheapest way to store 48 gallons of water is to buy a plastic drum. While this was easy and cheap, it complicated the problem of heating the water. The drums are made of a plastic that does not like to get hotter than 180 °F. This will complicate the design of my heating system, but not too much.

### Heating the Lake Water

I had heard another engineer mention that he had heated molasses in a 55 gallon drum using a drum heater belt (example). This sounded like the perfect solution to my problem. There were two concerns with the heater belt:

• Could I use a heater belt with a plastic drum?
• How fast would it heat the water?

#### Using the Heater Belt with a Plastic Drum

In the interest of full disclosure, I first bought a metal 55 gallon drum and a metal-drum heater belt. Unfortunately, the metal drum really began to corrode, and the rusty smell and appearance of the water was drag. That is when I switched to a plastic drum. I had seen a plastic drum heater. It was very similar to a metal drum heater, but with a large metal band around it to spread the heat out. The plastic drum heater was much more expensive than the metal drum heater, and I already had a metal drum heater. So I took my plastic drum, bought a \$5 roll of aluminum tape (the kind used on ducts) and I wrapped the middle of my plastic barrel with the tape (see figure below). I made the tape layer much wider than the heater belt to spread the heat out. It has worked well.

#### How fast will the Water Heat?

The belt is powered from a 120 V outlet (standard US voltage) and puts out 1500 W. Because the belt wraps around the outside of the barrel, some of the heat is lost to the environment. This makes heating the barrel a bit inefficient, but workable for my needs.

${t_{Heat}} = \frac{{V \cdot \rho \cdot \kappa \cdot \left( {{T_{Desired}} - {T_{Lake}}} \right)}}{{k \cdot R}}$

where

• TLake is the temperature of the lake water (assume 55 °F for a spring or fall temperature)
• TDesired is the temperature we want for showering (105 °F)
• $\rho$ is the density of water (1 gm/cm3
• $\kappa$ is the specific heat of water (4.187 J/gm °C)
• R is the rate of heat generation (1500 W)
• k is the efficiency of heat transfer from the barrel to the water (75% a guess)
• tHeat is the time to heat the water to TDesired from TDesired.

Plugging all these numbers into the equation gives me ~5 hours, which is about what it actually takes during the cold times with a large number of people. During the warmer times with fewer people at the cabin, I cut the amount of water in the drum. This reduces the heating time to a couple of hours. All these numbers have proven manageable.

### Designing the Shower

Nothing real sophisticated here. I put together a quick water pump/shower system with the following equipment:

• a 12 V DC recreational vehicle water pump
• a 12 V power source, something nice and safe. The safest is a battery, but that needs to be charged. There are numerous 12 V power sources on the market.
• some garden hose
• a shower nozzle that screws on the end of the garden hose (any hardware store has this nozzle).

I made the shower enclosure out of some landscape fencing material that I found cheap at a Home Depot. The completed shower assembly can be seen in the photo below.

### Removing the Gray Water

The procedure here was straightforward as well. Here is what I did:

• Built the floor base Durock (Durock is a common wallboard used for showers)
• Cut a drain hole in the Durock and put in a floor drain I picked up from the hardware store
• Coated the Durock with waterproofing paint mixed with sand
• Connected up 30 feet of flexible drain tile to the floor drain.
• Buried the drain tile on a downward slope (my whole cabin sits on sand)

The whole shower has been working now for at least 5 years and still looks good. I have included photos of the shower hardware and the shower enclosure. It functions well and it makes living at the cabin a bit more comfortable.

 Mechanical Hardware for the Lake Water Shower Shower Enclosure
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### 2 Responses to My Little Gilligan's Island - Part 1 (The Shower)

1. Susan Broqvist says:

Hi, we have a cabin that is similar to yours and in close proximity to the lake. We only use the cabin in the summer but it takes a long time for the lake water to heat up as we are in Sweden. I am wondering if there something as a solar shower - heated up by the sun. We usually bath in the lake but a shower would be nice once in while - especially on rainy or cold mornings (which we have here a lot). btw - we have no electricity. is there a way to maybe have a solar heater to warm up the water (barrel?). I'm just hoping that there might be something we can 'rig up' to work. Thanks! Susan

• mathscinotes says:

There are many solar shower options. Here is a solar shower that is commonly seen in the US. Unfortunately, it is a bit small. However, it does work for a single person.

I am currently working on a solar water design for my cabin. I will write about this in a few months.

Mathscinotes