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Cargo Capacity Calculation

Discussion in 'Gen 4 Prius Technical Discussion' started by Tideland Prius, Nov 3, 2016.

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  1. Tideland Prius

    Tideland Prius Moderator of the North
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    Alrighty. Here's my very rough take on the cargo capacity calculation of the Gen 4 Prius with a spare tire. @wjtracy and @bwilson4web. Please take a look at my numbers and double check the calculations (taking in account my assumptions).

    Recall:
    Europe/Japan: 457 litres or 16.1 cu. ft.
    US/Canada: 697 litres or 24.6 cu. ft.

    I apologise for the small font size in the diagram so here they are listed:

    Length:
    ~84.0 cm - average length of floor from bumper to seatback
    70.8 cm - length of cargo area from rear hatch to top of seatback at the side of the cargo area

    Width:
    95 cm - Width behind the seatback on the floor
    110 cm - Width behind the seatback at the top of the seatback
    146.5 cm - Maximum width at the enclaves

    Height:
    35 cm - Height of floor to plastic area (so the height of the carpeted area)
    39.6 cm - Height of floor to approximately the rear spoiler height. (Or, the maximum height that will fit with the hatch closed)
    ~63.5cm - Maximum height of the cargo area from floor to ceiling behind rear headrest (I measured to the rubber seal)

    Rear glass area:

    Maximum length = 130cm
    Maximum width = 52.3cm
    Approximate depth = 8.3cm (this is what I measured from the rear glass to approximately an invisible flat plane across the plastic frame of the rear hatch. This is needed to calculate the volume. I can also then use this invisible flat plane as one of the surface for a triangle to calculate the volume above the tonneau cover).




    IMG_7924.JPG


    Obviously the cargo area is made up of complex shapes so there are many approximations and assumptions made, but here goes.

    1. Maximum volume of a simple box that will fit in the cargo area with the hatch closed (so slightly above the tonneau cover but below the rear spoiler and behind the rear seat):

    lxwxh = 70.8*95*39.6 cm
    = 266349.6 cm³
    = 266.3496 L (I'll jump straight to litres from the next calculation onwards)

    2. Area of triangle between the top of the rear seatback and the bottom of the rear seatback

    Floor length ~84.0cm
    Top of seatback length 70.8cm

    Difference = 13.2cm

    Width = 95cm at the floor

    Volume = 1/2*13.2*95*39.6

    =24.8292 L

    3. Enclaves are very much approximated so assuming a cylinder (cause each one is half a cylinder)

    Diameter = maximum width - width of main cargo area = 146.5cm - 95 cm = 51.5 cm

    Therefore radius = 25.75cm

    pi (r)² h = 3.1415626*(25.75)²*35
    = 72.907 L (obviously the two enclaves put together is more like an oblong shape as the diameter is wider in the middle than at the top or bottom, as well as the height slopes down towards the sides of the cargo and we were using the maximum height)

    4. In step 1, we were using a simple rectangular box placed on the floor. The top of the cargo area is wider, so now we'll calculate the triangular volume between the sides of the imaginary box and the sloped cargo area.

    Base of upside down triangle = max width - floor width

    = 110-95
    = 15cm

    Recall height is 39.6cm
    Length, we'll use the top of the seatback*, so that's 70.8cm

    1/2*15*39.6*70.8
    = 21.0276 litres. But there's both sides of the car, so multiply by 2
    = 42.0552 L

    *Right now, I've ignored the tiny area we missed out at the extreme edges of the cargo area behind the rear seatbacks. I *think* it's small enough to be negligible since the cargo area is nearly vertical for the first half from the floor, due to the double wishbone suspension intrusion. Only after that does it widen as you go up in height towards the top of the seatback. Might be worth half a cubic foot? (both sides)


    For those keeping tally, we're at 406.141 litres or 14.34 cu. ft.

    Now to calculate the approximate maximum volume

    5. Triangular area between the sloping rear window (recall that imaginary flat plane I was using earlier in the measurements discussion), the rear seatback and the rear plastic piece between the rear window and the lower rear glass.

    Max height = 63.5cm
    Height previously used = 39.6cm
    Remaining height of triangle = 23.9cm

    1/2*70.8*110*23.9 cm = 93.0666 L

    6. Very, very approximate volume of the space above the triangle calculated in Step 5 and the rear window glass

    130*82.3*8.3 cm = 56.4317 L


    Total approximate volume = 406.141 + 93.0666 + 56.4317

    = 555.6393 L
    = 19.622 cu. ft.

    Still off from the 697L /24.6 cu. ft. BUT, because the cargo floor is curved near the rear bumper, there's that volume we missed out (because we used a box so add ~ 0.5-1 cu ft) AND there's the volume of the space underneath the spoiler where the lower rear glass is (approx 1 cu. ft.) AND there's the volume between the rear headrest, roof and the top of the rear seatback that I missed out (1-2 cu ft) and make adjustments to the enclaves.

    If I were just to tally up the usable space, I'd get very close to the Japanese/European estimated volume of 457 litres (16.1 cu ft). I think my total is 15 plus the rear glass which I know is an overestimation in my math above.


    Conclusion?

    The European/Japanese spec of 16.1 cu. ft. for the Gen 4 w/ spare tire is the usable space (e.g. if you were to fill it with luggage or boxes or stuff that are regularly shaped)

    The US/Canadian spec of 24.6 cu. ft. is literally the maximum volume you can carry (e.g. you stuffed all the nooks and crannies with soft, irregular items)
     
    #1 Tideland Prius, Nov 3, 2016
    Last edited: Nov 4, 2016
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  2. alanclarkeau

    alanclarkeau Senior Member

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    And because mostly, when we're in "CRAM MODE" we put in suitcases or boxes, I'd suspect 16.1 cu ft is the most useful. I wonder if I've got a foot ruler any more, so I'll go with your 457 litres. Which is what TOYOTA reckons here too.

    In most cases here, Manufacturers use what is referred to as "Litres VDA", though some still use SAE (I think it was Jeep & Chrysler still using it). I read that VDA is German for (abbreviated description) how many "blocks of wood measuring 200mm x 50mm x 100mm" will fit.
     
    #2 alanclarkeau, Nov 3, 2016
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  3. wjtracy

    wjtracy Senior Member

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    Tideland-
    ...hmm. but I am not thinking the only difference between EPA cargo space and "true" volume is simply nooks and crannies. For example, Volt is 11.x true ft3 and 19.x ft3 EPA method.

    For Gen4, you have previously posted Toyota USA data sheets, showing:

    "Luggage Space" 16.1-ft3 and 17.7-ft3 for Level 3/4
    "EPA Cargo Space" 24.6-ft3 and 27.4-ft3 for Level 3/4

    This also goes back to the original Toyota Japan Gen4 Powerpoint slides showing 502-liters (17.7-ft3) for Gen4.

    I wonder if we could ask Toyota Team or Toyota Japan to comment on these seemingly contradictory numbers. I'd like to to know if Luggage Space as defined by Toyota is actual ft-3 volume e.g. from CAD drawings, or VDA method (block loading technique).
     
    #3 wjtracy, Nov 3, 2016
  4. Trollbait

    Trollbait It's a D&D thing

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    Unlike MPG figures, manufacturers aren't required to use the interior volume figures they submit to the EPA in marketing materials.

    The Volt's 11.x ft3 listed on the Chevy site is likely the volume under the tonneau cover. The EPA figure will include the space above that.
     
    #4 Trollbait, Nov 3, 2016
  5. Tideland Prius

    Tideland Prius Moderator of the North
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    Why not? 8 cu. ft. difference in the Volt is enough to cover the nooks and crannies, no? As if you were filling the cargo space with liquid (or a gas).

    Minor detail, but in the Japanese press release (the ppt slides you're referring to), the cargo area behind the seatback is sloped at the same angle as the seatback from floor to ceiling. However, if you stop at the top of the seatback and continue vertically up instead of at a slant, you'll gain some volume there too.
     
    #5 Tideland Prius, Nov 3, 2016
  6. wjtracy

    wjtracy Senior Member

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    ...i am not convinced...As I previously pointed out, my feeling is GM wants to use real cargo space (11.x-ft3) so they can show passenger space in the respectable 90+ft3 area. If GM had to quote 19.x ft3 cargo space, they'd only be able to show 80-ft3 passenger space (total space minus cargo). In reality I suspect the Volt passenger space is truly in the low 90's ft3 and that leaves a true 11-ft3 left over for the cargo quote. Prius, with much more total space, does not mind over-quoting cargo space in the US market which still gives say 93-95 ft3 passenger space.

    The interesting thing I noticed was only USA seems to quote Total interior space. EU they only quote VDA cargo space with no total car interior volume at least the on line specs I see. If we have that Total, it might help.
     
    #6 wjtracy, Nov 3, 2016
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  7. Tideland Prius

    Tideland Prius Moderator of the North
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    40 CFR 600.315-08 - Classes of comparable automobiles. | US Law | LII / Legal Information Institute

    Based on that, the cargo volume will be somewhere around 15 cu. ft. (with spare tire)

    Interestingly, Acura lists both types of measurements (but they're only 1 cu. ft. apart, not 8.

    2017 Acura MDX | Specifications | Acura.com
     
    #7 Tideland Prius, Nov 3, 2016
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  8. Trollbait

    Trollbait It's a D&D thing

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    I don't understand how you are arriving at this conclusion.

    The cubic foot volume figures for the Volt at Fueleconomy.gov is 90 for passenger and 19 for cargo. On Chevy's site they are 90.3 and 10.6. The difference between the passenger specifications is just due to rounding. There is a 8.4 cubic foot difference between the cargo specs, which can't be explained by rounding. Since the Volt has a shallow slant to its hatch, leaving the car with a profile close to a sedan's, it is possible GM is only measuring the space from the floor up to the top of the rear seat, because the space above that isn't as usable as it would be in a hatchback with a squarer rear. Which leaves those 8.4 simply on counted.

    None of that missing space has been applied to the passenger volume though, as you imply here and elsewhere

    The EPA uses total interior volume as metric for assigning cars to its different size classes. This isn't so in Europe. In fact, beyond passenger car, there doesn't appear to be any official size classes for cars. There are ones for marketing, but it seems assignment is subjective; the Corolla is a small car because it is smaller than the Camry.
     
    #8 Trollbait, Nov 3, 2016
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  9. wjtracy

    wjtracy Senior Member

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    TB- I don't FuelEconomy.gov is a good place to go for space quotes...the 19 is not consistent with the 90ft3. It is mixing apples and oranges (different measurement bases). In fact is exactly what I think EPA wants is to give green cars a chance to claim vol that is not there.
     
    #9 wjtracy, Nov 3, 2016
  10. Trollbait

    Trollbait It's a D&D thing

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    How is it not consistent? Is there an EPA total volume value for the Volt printed elsewhere? Besides your distrust of the EPA system, do you have any evidence on why we can't take them, or GM, at face value? Why does the discrepancy between the cargo measurements have be the result of something shady, and not simply because GM choose to ignore a part on the volume for their marketing materials? Claiming midsize would benefit the Volt more than being a compact with a few more cubic feet.

    The EPA system isn't perfect, but the flaws extend to all cars. It is a measure of the car's interior space. The only effect that the drive train will have is in how much it protrudes into that space. The wiggle room in the measurement standard can be applied to ICE, hybrid, or plug in. Green or dirty matters not.
     
    #10 Trollbait, Nov 3, 2016
  11. wjtracy

    wjtracy Senior Member

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    The FuelEconomy.gov website would have to be very specific about measurement basis to be accurate. Does it say EPA Passenger Space/EPA Cargo Space? I don't think so ...it just has generic Luggage Space and Passenger space so you got apples and oranges, with freedom for someone to pick their favorite numbers by different specs.

    Look at this (presumably accurate) GM info:
    GM: Volt has 90.3 ft3 Passenger Space and 10.6 ft3 Cargo Sapce
    2017 Volt Trims: Premier - LT | Chevrolet

    EPA says it has 90 ft3 passenger space and 19 ft3 Cargo space. EPA are mixing apples and oranges, using whatever technique shows the best numbers...but if they do that, they need to be consistent.
     
    #11 wjtracy, Nov 3, 2016
  12. Tideland Prius

    Tideland Prius Moderator of the North
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    @wjtracy, I think @Trollbait 's got it right though.

    For government purposes, you need to provide the total interior volume for a hatchback to get the size classification.

    For marketing, you can use whatever the heck you want but obviously it cannot be more than the (EPA) cargo volume that they provided to the government.

    Chevrolet decided to provide "usable" cargo space (without blocking the view out the rear window) while Toyota decided to provide maximum cargo space. Both manufacturers are right.
     
    #12 Tideland Prius, Nov 3, 2016
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  13. Trollbait

    Trollbait It's a D&D thing

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    Fueleconomy.gov is maintained by the EPA. The values for space posted there are the ones the manufacturer submitted to them, as measured by the required standard. A wrong value being posted is possible, but modifying official numbers intentionally shouldn't be a regular suspicion. Might as well assume the site is lying about MPG figures too.

    Legally, the auto company can only use the EPA certified MPG figures in marketing materials. There is no such legal requirements in regards to the interior volumes. A company can use the same values they submitted to the EPA, or they can use values derived in a different manner. The SAE method required for the EPA has been updated multiple times since it was made the official version. Some companies use the newer versions for marketing, because they give a better estimate of the usable space than the official EPA one.

    Then there is nothing stopping from not measuring the entire space if they choose too. Nor are they prevented from applying the standard for trunks or the European standards for their advertising of the car. Without a footnote to the value naming how it was obtained, we are left guessing. The only thing truly limiting what a company presents for interior space in marketing material in the US is misleading advertising laws.
     
    #13 Trollbait, Nov 4, 2016
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  14. wjtracy

    wjtracy Senior Member

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    Well you guys got me outnumbered, and I must admit it is confusing and I do not have all the answers. This is where we need Consumer Reports or somebody to step in and check the numbers, but they do not seem to want to take it on.
     
    #14 wjtracy, Nov 4, 2016
  15. Tideland Prius

    Tideland Prius Moderator of the North
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    Well there's this

    How Consumer Reports Tests Cars - Consumer Reports

    So it looks like they go for maximum usable space (i.e. what's the biggest box that will fit or for sedans, what's the maximum number of suitcases that will fit). That's a third option lol.
     
    #15 Tideland Prius, Nov 4, 2016
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  16. wjtracy

    wjtracy Senior Member

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    Does that mean we have CR Cargo Space as well as CR MPG?
    But I do not recall seeing any CR data. I have CR account so I will check and get back.
     
    #16 wjtracy, Nov 4, 2016
  17. Trollbait

    Trollbait It's a D&D thing

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    This is a variation on the EPA trunk and EU VDA cargo measurements. The difference being those use a set sized box instead of actual luggage to fill the cargo area.
     
    #17 Trollbait, Nov 4, 2016
  18. Tideland Prius

    Tideland Prius Moderator of the North
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    *Except for sedans. They still use luggage for that.
     
    #18 Tideland Prius, Nov 4, 2016
  19. wjtracy

    wjtracy Senior Member

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    Somebody please call me a doctor!
    Here is Volt/Prius Cargo Capacity, Consumer Reports style

    2016 Gen4 Three: 2 Big bags + 2 Small bags
    Plug-in PiP: 3 Big Bags
    Gen3 & Gen2: 3 Big Bags and 1 small bag

    Volt 2016: 2 Big Bags (did we lose some vol for 2 small bags? see below)
    Volt 2015: 2 Big Bags and 2 Small Bags
     
    #19 wjtracy, Nov 4, 2016
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  20. Tideland Prius

    Tideland Prius Moderator of the North
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    The Prius volumes sound about right, don't they? Based on what you calculated a few months ago.

    I'm not sure about the Volt. I suspect the Prime will be 2 big bags or at most 2 big bags + 1 small bag (depending on how tall the big bags are when laid on their side cause there's potentially a height issue with the dual wave glass)
     
    #20 Tideland Prius, Nov 4, 2016
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