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Old 05-15-2012, 06:20 PM   #1 (permalink)
christofoo
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00C - '00 Toyota Corolla
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Minimum grill opening requirement

I worked up a spreadsheet that (supposedly) calculates a grill opening requirement. ...I couldn't find this calculation elsewhere so I'm assuming this is helpful...

EDIT 1/6/13: I added a term for the loss of heat through the exhaust gas. This matters because the exhaust gas is much much hotter than the radiator, so although it is a smaller volume it represents about 20% of the total thermal load. Therefore my new area calcs are about 20% lower than previously.

My purpose is to help guide grill block design (since I'm doing one soon). I.e. how far does your grill need to open and under what conditions can you expect it to be required?

I think it's particularly crude since I don't know how much the radiator actually heats the air that passes through it, but I'm making an assumption so I can use the specific heat of air to determine heat dissipation for a given flow rate. Most likely the openings I calculate are low for that reason, but they are probably not so terribly off to be a bad reference point.

It'd probably be good if someone can check my work. I checked my drag force against the one on the wiki, and most of what else I did seems straight forward, but who knows?

Assuming it's all correct, here is some tabulation of typical results: EDIT 1/6/13 I corrected the values to include heat lost through the exhaust gas. I also thought that 22% for ICE thermodynamic efficiency is low and used 28% instead, an important rationale is that cooling requirements are most stringent while climbing, but in that condition throttle loss will be low and thermodynamic efficiency will be higher than normal. For the 0% grades I backed off to 25%, which may be reasonable for economy cars but not sportier cars. The net result of both changes is almost a 50% reduction in my grille area suggestions below:
  • Sustained 5% grade climb at 65MPH, 3,000 lbs gross weight, 120F ambient, 15MPH tailwind, 5,000ft elev., 2kW AC: 167in^2 (4.5in^2/hp) 89in^2
  • Sustained 5% grade climb at 65MPH, 3,000 lbs gross weight, 120F ambient, 0 tailwind, 5,000ft elev., 2kW AC: 141in^2 (3.5in^2/hp) 81in^2
  • Sustained 5% grade climb at 65MPH, 3,000 lbs gross weight, 100F ambient, 0 tailwind, 0ft elev., 1.5kW AC: 96in^2 (2.2in^2/hp) 56in^2
  • Sustained 3% grade climb at 65MPH, 2,500 lbs gross weight, 100F ambient, 0 tailwind, 0ft elev., 1.5kW AC: 66in^2 (2.3in^2/hp) 38in^2
  • 0% grade, "loaded sedan" at 75MPH, 100F ambient, 0 tailwind, 5,000ft elev., 0kW AC: 48in^2 (2.2in^2/hp) 32in^2
  • 0% grade, "loaded sedan" at 75MPH, 40F ambient, 0 tailwind, 5,000ft elev., 0kW AC: 30in^2 (1.3in^2/hp) 20in^2
  • 0% grade, "aerocivic" at 70MPH, 40F ambient, 0 tailwind, 0ft elev., 0kW AC: 15in^2 (1.1in^2/hp) 10in^2

(I think this spreadsheet is also less accurate when you're not climbing, because it assumes that the air through the grill is the only means of cooling, which is more true when the cooling demand is very high (lots of horsepower in use), and it's particularly untrue at low ambient temperature and of course the whole premise is false if your trip is short.)

(Note that where I write in^2/hp I'm referring to wheel output hp. I get the feeling that I must be typically climbing at least 2X below my Civic's "specified" engine power output for some reason, maybe because I don't like the sound of high RPMs and like to keep it in 5th mostly, and use 4th for pulses when I drop below 60MPH.)

Conclusions (not surprising):
  • Need it wide open for absolute worst case, climbing north towards Flagstaff in summer heatwave with a tailwind (hint: avoid that scenario).
  • Need a good size opening for climbing passes in inland summers.
  • Need a minimal-to-modest opening for flat ground in the summer (also requires a decent sized opening for AC condenser if used, not calculated here, note AC compressor efficiency will suffer if the opening for the condenser is too small, so engine load penalty may be higher than aero gain for all you AC users).
  • Leave it closed for flat ground below freezing (probably).
  • Cd reduction will also have the effect of reducing grill opening requirement on flat ground, since it (obviously) reduces engine output. Not as true during sustained steep climbing.
  • Weight reduction will have the effect of reducing grill opening requirement while climbing. Not as true on flat ground.

BTW, this is my first time posting here, but I have really enjoyed this site since I found it earlier this year. I've been hypermiling since 2007 and I really wish I'd found this site earlier. I'm now nearly finished with phase I of my aero mods on my Civic (wheel slicks and passenger mirror delete). Phase II will be front end and wheel skirts. For phase III I'm thinking I will make a partial-boattail-type shell for my hitch-mounted luggage rack that my family of 4 uses on long hauls. (Sooner or later I'll put my stuff in the ecomodder garage too.)

Attached Files
File Type: xls GrillArea.xls (29.0 KB, 80 views)
File Type: xls GrillArea_wExhaust.xls (13.0 KB, 89 views)

Last edited by christofoo; 01-06-2013 at 04:28 AM.. Reason: inclusion of exhaust gas heat loss rate
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