Aerodynamics Seminar # 6 - by Phil Knox

[RH77]

Don't forget that air density and baro-pressure change as altitude increases.

For aircraft, since baro-pressure is very unreliable at higher altitudes, the standard 29.92 mm Hg is set at 18,000 feet and the call is Flight Level 1-8-0 instead of 1-seven-thousand, niner-hundred feet or lower...

Similarly, since the air is less dense at higher altitudes, the pitot tube can no longer be reliable to report the passing air molecules. Ground speed increases with the decrease in resistance, but the airspeed indicator vs. altitude has to be compared to aircraft documentation/reference , as to not induce an overspeed and consequent aircraft overstress situation. Comparisons to GPS (if equipped), should provide the most accurate velocity.

RH77

[boxchain]

Originally Posted by trebuchet03

v^2 for force... Power is Force*Distance - which is where the extra v for v^3 comes from

OK, plugging those in, I get 5-51kW, or 6.8-68 hp from 35-100mph. Sounds more reasonable. Graph looks nicely non linear too.

[Harpo]

I get twice the HP required at 70mph as compared to 55mph. I'm sure fuel flow follows that same relationship?

I guess an extra mile on a 25 mile trip to avoid 70mph traffic is almost worth it's weight in gold.

[RH77]

Originally Posted by Harpo

I guess an extra mile on a 25 mile trip to avoid 70mph traffic is almost worth it's weight in gold.

Welcome to the site, BTW (don't think I've done that yet )

But yeah, that extra mile at slower speeds can make the difference providing it doesn't involve the potential for stop-and-go, or added consumption beyond the baseline trip.

What I inadvertently performed in the past was to take backroads in the last 10 miles of a 30 mile trip. I attained better FE since slower speeds were involved, but I ended up using more fuel because there were 4x as many traffic lights. It was a crap-shoot, and on the best day, it still used more fuel -- but with a higher avg. FE.

[boxchain]

Originally Posted by GenKreton

I'm not sure what the second part of the equation is, the addition, but in order to add numbers, the units MUST match. Pmotive=1/2*Cd*A*rho*v^3 is normal for a flat surface. What is Crr1?

Crr1 is the coefficient of rolling resistance. This is linear w.r.t. weight and speed, and becomes a small factor in the equation at speed when the air effects dominate.

[boxchain]

Originally Posted by optiwatch

Understanding that HP to overcome aero/drag is helpful. I want to include vehicle weight in my calculations to fully understand the impact of weight.

BTW this spreadsheet is ONLY for cruising speeds, where weight is somewhat insignificant. Weight plays a much bigger part of the picture when you're looking at acceleration. For that, use F=ma

[aerohead]

Originally Posted by boxchain

Those numbers sound reasonable. I used the spreadsheet and tried to stick with metric and I got 3.4 kw @ 35 mph and 10.3 kW @ 100 mph, which translates to 4.5 and 13.8 hp. Maybe I got some conversions wrong though.

slugs! *groans*

I always thought it was v^2 not v^3, just from what I remember from my fluid mechanics class.

v^2 will yield force,v^3 will yield power necessary to overcome the force.

[roflwaffle]

Originally Posted by Harpo

I get twice the HP required at 70mph as compared to 55mph. I'm sure fuel flow follows that same relationship?

I guess an extra mile on a 25 mile trip to avoid 70mph traffic is almost worth it's weight in gold.

Possibly. The thing is, engine efficiency increases with load/HP, although in most cases not as fast as load/HP with speed, so in most cases it's better to drive slower in the same gear. However, if someone wants to see the full effect of the decrease in HP from 70mph to 55mph they will likely need to break up the power output into chunks to maximize efficiency.

[optiwatch]

Originally Posted by GenKreton

Let's stick to the metric system since it seems to use it, mostly?

1/2C_d is unit-less
A in m^2
rho is density, so kg/m^3
v is m/s, so v^3 is m^3/s^3

so we have kg*m^2/s^3
1 N is kg *m / s^2 -> Nm/s
1 J is Nm -> J/s
1 W is J/s, so we are left with pure watts
1 hp is 0.7457 kW

Essentially we take the result of the first part and *10^-3 / 0.7457, or multiply by 0.01341.

I'm not sure what the second part of the equation is, the addition, but in order to add numbers, the units MUST match. Pmotive=1/2*Cd*A*rho*v^3 is normal for a flat surface. What is Crr1?

Apologies for the long time to respond. Crr1 is the rolling resistance of the tires. Thank you for the detailed formula breakdown. I also looked at the updated spreadsheet boxchain provided. All this information provides a much clearer picture.

Thanks again!

[Stan]

Originally Posted by Harpo

I get twice the HP required at 70mph as compared to 55mph. I'm sure fuel flow follows that same relationship?

That doesn't sound right. My Golf TDi gets 50 mpg at 70 mph and 63 mpg at 55 mph. That's about a 25% change...not 100%. Stan