Tag Archives: turbulence

Golfball dimples on a car for improved mpg.

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The Mythbusters dimpled Taurus, and a diagram meant to show how drag is reduced. On a golf ball, at low NRE, vortex separation is moved back to 110°, the mechanism on a car is different, I suspect.

The dimples on a golf ball reduce air-drag resistance, so why don’t we put dimples on planes or cars? Perhaps because it’s ugly, or that cars are much bigger and than golf-balls, so we expect the effect of skin effects to be smaller. Finally, a Reynolds number analysis suggests that dimples on cars should increase drag, not reduce it.

In 2009, the Mythbusters decided to test the conjecture. Hosts Jamie Hyneman and Adam Savage ran careful gas usage tests on a Ford Taurus that was first covered with smooth clay. They drove the car repeatedly (5X) on a track at 65 mph (about 100 km/h), and measured “slightly over 26 mpg,” 9.047 l/100km, a respectable value. They then carved dimples into the clay to simulate the surface of a golf ball. See picture at right, and put the removed clay into the trunk so there would be no decrease in weight.

Underneath a Porche GT4, smallish dimples.

They then drove the dimpled car over the same course, five times as before at exactly 65 mph, and found the car got 14% more mpg, 29.6 mpg, or 7.946 l/100 km. See video excerpt here. They considered it their most surprising Mythbuster episode.

As it happens, dimples had been put on some production cars, even before the episode. They are just located underneath where most people don’t see them. The VW “Golf” had dimples even before the episode, and the Porsche Cayman GT4 does today, see picture above left, but most experiments find little or nothing. Car dimples are typically smaller than those used on Mythbusters, so that may be an explanation. Dimples have been found to help on soccer balls (the stitching acts as the dimples), and bicycle wheels (less advantage).

PHYSICS OF FLUIDS 18, 041702 (2006) Mechanism of drag reduction by dimples on a sphere, Jin Choi, Woo-Pyung Jeon, and Haecheon Choia.

The graph at right shows the source of confusion for cars and the great advantage for golf balls. It’s a plot of the drag coefficient for smooth and dimpled golf balls, as a function of the Reynolds Number, where NRE = Vdρ/µ. In this formula, V is velocity, d is the diameter of the car, ball or whatever, ρ is the density of the fluid, and µ is viscosity. NRE can be thought of as the ratio of the inertial to viscous forces acting on the object. It’s a way of describing the combined effects of speed and size for different objects in motion.

We see, above, that dimples reduce golf-ball drag by more than 50%, but only at speeds/ Reynolds numbers that are much lower than for normal cars, NRE between about 4×104 and 3.5×105, as are typical of golf balls during play. A typical car at 65mph will have a NRE.CAR = 3×106, suggesting that there should be no advantage for dimples, or possibility a disadvantage, that dimples should increase drag. A side note one sees, above, is that it is only the dimples on the front of the golf-ball that reduce drag: other dimples do nothing. If one were to add dimples to high-speed trains and airplanes I’d suggest them only on the front, so far I have not seen them.

I think that the Mythbusters did a good job with their experiments, and find their 14% improvement significant. So why do so few other cars see and advantage. One thought I had was to note that the Ford Taurus is a remarkably round car, providing ample space for front dimples to help, most cars today are more angular. I also note that the production cars have smaller dimples, as on the Porsche, above. Then again, the Mythbusters folks may have made some non-obvious experimental error.

Robert Buxbaum, January 4, 2024. An important side issue in this is that Google’s AI was awful, a handicap in researching this article. It lies continuously and convincingly, and did so here. I’d asked it for the year of the episode, and the AI lied, and said 2012. I asked for the type of car, the AI said an SUV, and it gave a misdescription of the tests. Lying AIs appear as villains in science fiction, e.g. HAL of 2001 A Space Odyssey, now in real life.

What drives the gulf stream?

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I’m not much of a fan of todays’ kids’ science books because they don’t teach science IMHO. They have nice pictures and a few numbers; almost no equations, and lots of words. You can’t do science that way. On the odd occasion that they give the right answer to some problem, the lack of math means the kid has no way of understanding the reasoning, and no reason to believe the answer. Professional science articles on the web are bad in the opposite direction: too many numbers and for math, hey rely on supercomputers. No human can understand the outcome. I like to use my blog to offer science with insight, the type you’d get in an old “everyman science” book.

In previous posts, I gave answers to why the sky is blue, why it’s cold at the poles, why it’s cold on mountains, how tornadoes pick stuff up, and why hurricanes blow the way they do. In this post, we’ll try to figure out what drives the gulf-stream. The main argument will be deduction — disproving things that are not driving the gulf stream to leave us with one or two that could. Deduction is a classic method of science, well presented by Sherlock Holmes.

The gulf stream. The speed in the white area is ≥ 0.5 m/s (1.1 mph.).

The gulf stream. The speed in the white area is ≥ 0.5 m/s (1.1 mph.).

For those who don’t know, the Gulf stream is a massive river of water that runs within the Atlantic ocean. As shown at right, it starts roughly at the end of Florida, runs north to the Carolinas, and then turns dramatically east towards Spain. Flowing east, It’s about 150 miles wide, but only about 62 miles (100 km) when flowing along the US coast. According to some of the science books of my youth this massive flow was driven by temperature according to others, by salinity (whatever that means), and yet other books of my youth wind. My conclusion: they had no clue.

As a start to doing the science here, it’s important to fill in the numerical information that the science books left out. The Gulf stream is roughly 1000 meters deep, with a typical speed of 1 m/s (2.3 mph). The maximum speed is the surface water as the stream flows along the US coast. It is about 2.5 metres per second (5.6 mph), see map above.

From the size and the speed of the Gulf Stream, we conclude that land rivers are not driving the flow. The Mississippi is a big river with an outflow point near the head waters of the gulf stream, but the volume of flow is vastly too small. The volume of the gulf stream is roughly

Q=wdv = 100,000 x 1000 x .5 =  50 million m3/s = 1.5 billion cubic feet/s.

This is about 2000 times more flow than the volume flow of the Mississippi, 18,000 m3/s. The great difference in flow suggests the Mississippi could not be the driving force. The map of flow speeds (above) also suggest rivers do not drive the flow. The Gulf Stream does not flow at its maximum speed near the mouth of any river.  We now look for another driver.

Moving on to temperature. Temperature drives the whirl of hurricanes. The logic for temperature driving the gulf stream is as follows: it’s warm by the equator and cold at the poles; warm things expand and as water flows downhill, the polls will always be downhill from the equator. Lets put some math in here or my explanation will be lacking. First lets consider how much hight difference we might expect to see. The thermal expansivity of water is about 2x 10-4 m/m°C (.0002/°C) in the desired temperature range). To calculate the amount of expansion we multiply this by the depth of the stream, 1000m, and the temperature difference between two points, eg. the end of Florida to the Carolina coast. This is 5°C (9°F) I estimate. I calculate the temperature-induced seawater height as:

∆h (thermal) ≈ 5° x .0002/° x 1000m = 1 m (3.3 feet).

This is a fair amount of height. It’s only about 1/100 the height driving the Mississippi river, but it’s something. To see if 1 m is enough to drive the Gulf flow, I’ll compare it to the velocity-head. Velocity-head is a concept that’s useful in plumbing (I ran for water commissioner). It’s the potential energy height equivalent of any kinetic energy — typically of a fluid flow. The kinetic energy for any velocity v and mass of water, m is 1/2 mv2 . The potential energy equivalent is mgh. Combine the above and remove the mass terms, and we have:

∆h (velocity) = v2/2g.

Where g is the acceleration of gravity. Let’s consider  v = 1 m/s and g= 9.8 m/s2.≤ 0.05 m ≈ 2 inches. This is far less than the driving force calculated above. We have 5x more driving force than we need, but there is a problem: why isn’t the flow faster? Why does the Mississippi move so slowly when it has 100 times more head.

To answer the above questions, and to check if heat could really drive the Gulf Stream, we’ll check if the flow is turbulent — it is. A measure of how turbulent is based on something called the Reynolds number, Re#, it’s the ratio of kinetic energy and viscous loss in a fluid flow. Flows are turbulent if this ratio is more than 3000, or so;

Re# = vdρ/µ.

In the above, v is velocity, say 1 m/s, d is depth, 1000m, ρ = density, 1000 kg/m3 for water, and  0.00133 Pa∙s is the viscosity of water. Plug in these numbers, and we find a RE# = 750 million: this flow will be highly turbulent. Assuming a friction factor of 1/20 (.05), e find that we’d expect complete mixing 20 depths or 20 km. We find we need the above 0.05 m of velocity height to drive every 20 km of flow up the US coast. If the distance to the Carolina coast is 1000 km we need 1000*.05m/20 = 1 meter, that’s just about the velocity-head that the temperature difference would suggest. Temperature is thus a plausible driving force for 0.5 m/s, though not likely for the faster 2.5 m/s flow seen in the center of the stream. Turbulent flow is a big part of figuring the mpg of an automobile; it becomes rapidly more important at high speeds.

World sea salinity

World sea salinity. The maximum and minimum are in the wrong places.

What about salinity? For salinity to work, the salinity would have to be higher at the end of the flow. As a model of the flow, we might imagine that we freeze arctic seawater, and thus we concentrate salt in the seawater just below the ice. The heavy, saline water would flow down to the bottom of the sea, and then flow south to an area of low salinity and low pressure. Somewhere in the south, the salinity would be reduced by rains. If evaporation were to exceed the rains, the flow would go in the other direction. Sorry to say, I see no evidence of any of this. For one the end of the Gulf Stream is not that far north; there is no freezing, For two other problems: there are major rains in the Caribbean, and rains too in the North Atlantic. Finally, while the salinity head is too small. Each pen of salinity adds about 0.0001g/cc, and the salinity difference in this case is less than 1 ppm, lets say 0.5ppm.

h = .0001 x 0.5 x 1000 = 0.05m

I don’t see a case for northern-driven Gulf-stream flow caused by salinity.

Surface level winds in the Atlantic.

Surface level winds in the Atlantic. Trade winds in purple, 15-20 mph.

Now consider winds. The wind velocities are certainly enough to produce 5+ miles per hour flows, and the path of flows is appropriate. Consider, for example, the trade winds. In the southern Caribbean, they blow steadily from east to west slightly above the equator at 15 -20 mph. This could certainly drive a circulation flow of 4.5 mph north. Out of the Caribbean basin and along the eastern US coat the trade winds blow at 15-50 mph north and east. This too would easily drive a 4.5 mph flow.  I conclude that a combination of winds and temperature are the most likely drivers of the gulf stream flow. To quote Holmes, once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.

Robert E. Buxbaum, March 25, 2018. I used the thermal argument above to figure out how cold it had to be to freeze the balls off of a brass monkey.