02
Jan
11

Complex systems and unexpected results

Race-car aerodynamics is a well-studied problem domain which is nonetheless as much an art as a science.  The interaction of uncounted billions of air particles with dozens of meticulously-shaped aerodynamic devices mere centimetres above the ground at speeds exceeding 200mph gives modern Formula One cars thousands of Newtons of downforce.  Millions of dollars, thousands of wind-tunnel hours, and zillions of teraflops have been spent trying to characterize, understand, and systematize these — individually relatively simple — interactions, and the aerodynamic sophistication of the 2010 F1 field makes it clear that formula-car aero is far better understood now than it ever has been.

And yet none of the other teams could match Adrian Newey’s RB6.  Simple Newtonian behaviour in (relatively-)incompressible flow is nonetheless complex enough that optimal solutions are very hard for even the world’s best aerodynamicists to design.

Much of this complexity comes down to the degree to which local changes affect global behaviour.  In Competition Car Aerodynamics, Simon McBeath describes a CFD experiment where two strakes are added to the underside of a formula car’s front wing, just inboard of the front tires.  This addition results in an overall increase in downforce of 0.5%, at the cost of a modest 0.1% increase in drag.  Not bad!

At the front of the car, the front wing shows a modest increase in downforce (0.3%) as the air under the wing’s mainplane is accelerated.  Similarly, the front tires generate just better than 50% less lift, perhaps because less of the front wing’s turbulent outflow is permitted to interact with them.  But strikingly, the rear wing is responsible for most of the increase in downforce, producing over 3% more with the strakes than without.  A change to the front wing produces its most striking results at the back of the car!

How can this be?  Even with a numerical simulation producing megabytes of data, McBeath is cautious about describing the causes of this result.  He notes that the strakes generate vortices on their inner faces, and suggests that these vortices encourage air to go over the car (increasing airflow under the rear wing’s mainplane) rather than under it; modest reductions in downforce at the front of the underbody corroborate this hypothesis.

Second-order effects (changes in airflow to the rear wing and underbody) dominate first-order effects (changes in airflow under the front wing)… in this case.  McBeath is careful to point out that small changes to the strakes’ shapes might produce different enough vortices to change the picture completely.

Formula-car aerodynamics, as forbiddingly complex as it is, pales in comparison to macroeconomics.  Financial reforms enacted in response to the credit crisis and widespread populist outrage against perceived usury drastically reduced the lending risks banks were allowed to take on and the fees credit-card companies were allowed to charge.  These changes were intended to reduce the amount of interest paid by borrowers with poor (or no) credit to banks and credit-card companies, and presumably they did so.

But once again, second-order effects dominate first-order effects.  Those poor-credit borrowers didn’t just stop borrowing when the banks couldn’t find a way to lend to them without too much risk and when Visa cut them off.  Instead, when the government decided to protect them from large institutions charging two-digit interest rates on long-term loans, they went to payday lenders charging three-digit interest rates on short-term loans.

Whoops!

In The Ascent of Money, Niall Ferguson talks about the disastrous effects of lack of access to respectable credit:

Only when borrowers have access to efficient credit networks can they escape from the clutches of loan sharks, and only when savers can deposit their money in reliable banks can it be channeled from the idle to the industrious or from the rich to the poor.  This point applies not just to the pour countries of the world.  It can also be said of the poorest neighbourhoods in supposedly developed countries — the “Africas within” — like the housing estates of my birthplace, Glasgow, where some people are scraping by on just £6 a day, for everything from toothpaste to transport, but where the interest rates charged by local loan sharks can be over eleven million percent a year.

Weren’t we just saying something about substitution effects being negative?  Credit cards are substitutes for bank loans; payday loans are substitutes for credit cards; and loan sharks (or privation) are substitutes for payday loans.

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13 Responses to “Complex systems and unexpected results”


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    .

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