Chapter 7 Causal Loop Diagrams -- 8 Exercises

Exercises 1-4: Managing the Electric Blanket

1. Complete the Diagram

Suppose you wish to draw a causal loop diagram to describe temperature control from an electric blanket. This system is similar to the home heating system discussed in the book. If you look to Figure 7.3 for ideas, you might draw this diagram. The loop on the left acts to control the heat flow to the sleeping space from the electric wires in the blanket. (A high dial setting means more heat production.) The loop on the right controls the heat loss. (Let's ignore heat from the sleeper's body.) Complete this diagram by labeling each arrow as + or - and each loop as (+) or (-).

2. Complete the New Diagram
The heat produced by the wires in the blanket depends on a dial which the sleeper may set between 1 (lowest heat) and 10 (highest heat). The dial setting is shown as an input to the previous exercise. Now, suppose you wish to expand the diagram to allow for changes in the dial position over time. Most people guess a setting when they first go to bed. For example, they might set the dial at "5", midway between the lowest and highest settings available. Then, after allowing some time for the heat flows to equilibrate, they might judge whether the equilibrium temperature is comfortable. If it's too hot under the blanket, they adjust the dial down. If it's too cold, they adjust the dial upward.

This diagram expands the previous diagram to represent these adjustments in the dial setting. A new variable (the temperature ratio) is defined as the ratio of the temperature under the blanket to the desired temperature. If the temperature under the blanket is 77 degrees and the desired temperature is 70 degrees, for example, the ratio would be 1.1 indicating that the temperature is 10% hotter than you would like. An observed temperature ratio is introduced to account for the delay in observing changes over time. The delay may be relatively short (i.e. you are still awake and are consciously delaying your reactions to allow time for temperatures to equilibrate). Or the delay may be long (i.e. when you are sleeping.) If the observed temperature ratio falls, the dial would be turned up. If it rises, the dial would be turned down. Complete this diagram by labeling each arrow as + or - and each loop as (+) or (-).

3. Two Sleepers and Two Blankets
Expand the previous diagram to include two people sleeping under two separate electric blankets. The sleeper on the left controls a dial on the left side of the bed. The sleeper on the right controls a dial on the right side of the bed. Your diagram should show a system with two sets of feedback loops that operate relatively independently of each other to achieve the separate goals. It should also show that the room temperature influences the heat loss from both blankets.

4. Misplaced Dials
Alter the previous diagram to represent the new system that could result if the dials are misplaced. Imagine that the normal system functions with the left dial at the foot of the left side of the bed while the right dial is located on the right side of the bed. Now, imagine that the dials become misplaced under the bed. Now, the sleeper on the left reaches down to a dial, but that dial controls the heat to the right side blanket. And the sleeper on the right reaches down to a dial that controls the heat to the left side blanket. How does your new diagram compare to the previous diagram? Do any of the loops in the previous diagram disappear? Do any new loops appear?

Exercises 5-6: The Private College Model

5. Feedback in the College Model
Recall the model of growth in a private college in the exercises for chapter 6. Draw a causal loop diagram to show the feedback loops in this model.

6. Structural Similarity
Find a model in Modeling the Environment whose feedback structure is similar to the previous exercise. Does the model in the book produce the same dynamic behavior as the model of the private college?

Exercises 7-8. The Hiking Models

7. Loops in 1st Hiking Model
Draw a causal loop diagram to shown the feedback loops in the 1st exercise with the four hikers.

8. Loops in 2nd Hiking Model?
Draw a causal loop diagram to show the feedback loops in model shown in the 2nd hiking exercise.
Do you see the same set of loops found in the 1st model?

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