Drafting experiment

I've posted a couple of times about drafting to increase fuel economy. And the Mythbusters have covered this as well. There seems to be no question that it's effective, witness the Tour de France and Nascar. So, what is the nature of the improvement?

I can only get better fuel economy if I have to overcome less force to go forward. Drafting certainly doesn't change rolling resistance or drivetrain losses, hence it can only affect aerodynamic drag. As I've discussed on previous occasions, aerodynamic drag, D, can be modeled by 

where rho is density, v is speed, Cd is drag coefficient, and A is frontal area. At a fixed speed (where Cd will also be constant) the only thing that can change is rho, the density. Thus, my working hypothesis is that drafting is effective due to a zone of lowered pressure behind the front vehicle.

I've purchased the Vernier LabQuest and a variety of sensors, one of which is the Gas Pressure Sensor which measures absolute (not gauge) pressure. I determined to see if I could measure this effect. I attempted to do so by cracking my window and extending the inlet tube of the sensor through the crack. My idea was to approach to and withdraw from the rear of the truck, recording my estimate of distance from the truck and the time as shown on the LabQuest display on my iPhone. I'd be looking for a reduction in measured pressure as I approached the truck.

So how did it go? Not so well. After multiple attempts, if anything, I recorded a trend to lower pressures as I moved away from trucks, higher as I moved in. And yet that can't be right. Or can it? This was a poorly designed experiment in that all factors that might affect the measured pressure were not controlled. My speculation is the confounding factor is the fact that I am on a freeway with hills and a general upward trend (I was eastbound, that is, away from the ocean toward the inland area). As I climb, the pressure will decline by about 0.012 kilopascals/meter and the range measured in the entire experiment was about 0.3 kilopascals, which would represent a climb of something like 25 meters. Now, the experiment was over a period of about 250 seconds and a driven distance of about 6 kilometers so such a variation in elevation is certainly not out of the question.

How can I get a better result? Since I don't have maps that indicate elevation and location with sufficient accuracy to adjust the pressure data to remove elevation changes, I can only think of two options. First would be to repeat the experiment in a controlled location. This is very difficult in that I don't have access to a truck and a suitable location. What else? My plan is to run the experiment and note the location, then to run it at the same location with no drafting. This should give me the ability to subtract out changes caused by elevation changes.  A negative result would cause major head scratching, stay tuned.

Economics - doomers and the BIG view

As I've previously expressed, I have a difficult time with economics (though I got A's in all my economics and finance courses in college). I think this is, at least in part, because it's abstracted from reality in that it's based on "money." Money necessitates a social structure such that something that has little or no actual value (greenbacks can't be eaten though I suppose they can be burned; electronic entries in a computer file don't even have this value).

There is a huge body of blogging (this last one uses the same template on blogger as I do) devoted to a doomer viewpoint predicting various degrees of collapse ot the economy and society. The consensus on such sites is that debt levels are completely unsustainable and will overwhelm all attempts to return to business as usual. Whether such a return is desireable is a different question but I think we can all agree that a return to a hunter gatherer society would not be. And if our doom is imminent, there are steps I need to take while I can.

So what is debt and when does it become unsustainable? In thinking about this, I find it helpful to ignore money. There is a certain amount of "stuff" that has been created by mankind and another, smaller, amount of stuff that has been returned to the universe in one form or another (solid, liquid, and gaseous refuse and heat). The difference is the amount of stuff we have collectively at this point in time. We use this stuff to sustain ourselves, to derive pleasure and comfort, and to create opportunities to get more and better stuff and to repay debt. Time engaged in productive (however one chooses to define it) activites is part of the stuff that we have. And there are other things that can't be touched that constitute stuff in this analysis. Movies, software, plays, and music come immediately to mind.

So, with this in mind, I think it's fair to characterize debt as a commitment to give some (greater) amount of stuff in the future in return for access to some (lesser) amount of stuff in the present. Upon assuming this debt, we decide to use some of it to derive sustenance, comfort, and pleasure and some to create opportunities to get more and better stuff. Whatever stuff is left over can be used to repay debt. Or, if you're the creditor, stuff should be used to repay debt followed by using it to create opportunities to get more stuff to enable the continuation of debt repayment and anything left over can be used to derive sustenance, comfort, and pleasure.

The last concept I need for my ultra-simplistic analysis is the concept of time value of money and discount rate. This captures the idea that it's better to have an amount of stuff now than the same amount of stuff in the future. The discount rate is that amount by which the value to get an amount of stuff one year from today is lowered from the value of getting the stuff today.

Thus, I'll theorize that debt and standard of living is sustainable if the World Gross Stuff Product ("WGSP") is sufficient to meet the continuing requirements of sustenance, comfort, pleasure, opportunity for stuff creation and have enough stuff left over to pay back the interest and principal of the borrowed stuff from newly created stuff. Is there enough stuff and are "we" continuing to produce enough stuff?

I'll need the following:

1. The total amount of stuff created (or mined, grown, etc.): S_c
   
2. The total amount of stuff discarded as waste stuff or waste heat: S_w
3. The rate of stuff use for sustenance: S_s
4. The rate of stuff use for new stuff creation: S_n
5. The effectiveness of creation of new stuff as a function of stuff used in its creation: dS_p/dS_n where S_p is stuff produced (or extracted or grown). Hopefully this will increase with time.
   
6. The rate of stuff production as a function of time: dS_c/dt (where t is time)
   
7. The rate of stuff "wasting": dS_w/dt
8. The discount rate for stuff: i (for interest)
   
9. The total amount of stuff owed in the future and the terms thereof: S_to
   

This will be my model, and with it I can speculate that we're sustainable as long as, for all t, there's sufficient stuff created to provide for sustenance, new stuff creation, and paying interest and principal on stuff. All I have to do is get data or approximations or estimates for those nine parameters. A large problem here is that they're mostly measured in money. But I have to proceed with this, there's really nothing better.


I'm well aware of the dwindling availability of easily and cheaply acquired concentrated solar energy in the form of crude oil, natural gas, and coal. But many of the doomer variety (and I do not use this noun disparagingly, I have doomer tendencies myself) predict doom even without such effects and so that's where I intend to start.

This analysis makes no account for the fact that the universe (not to mention the small portion of it to which we have access) cannot provide an infinite amount of stuff nor can it contain an infinite amount of waste. Nor does it account for the desires of a large portion of humanity to catch up with the rate of stuff creation and utilization enjoyed by the so-called "developed nations." It further takes no account of misallocation of stuff (the market is supposed to take care of that). And it ignores the possibility of increasing amounts of stuff having to be invested to procure the energy to create more stuff. Whatever conclusions may be reached, these considerations will certainly make them overly optimistic. However, I believe that manipulation of the parameters will provide guidance on where changes may be effective.


This project will, of necessity, be a fairly lengthy process upon which I'm just getting started. I'll post the results or, if it really takes a long time, status of progress. In the mean time, comments on the model are welcomed. If you're wondering why I've decided to post these thoughts now, it's because I haven't posted anything in almost a month.