# How much air does a square meter of sugar beet consume per hour?

I've come across a person who tried to disprove photosynthesis (yeah, I know). The basically took numbers of record sugar beet crop in Chile (192 tonnes per hectare), and tried to calculate how much air the plant would consume in order to grow. They've ended up calculating that a square meter of sugar beet field needs 7.32 cubic meters of air per hour, and they decided that this is too much, as it is amount 14 people breath in, hence their conclusion is the photosynthesis isn't real.

Where's the error?

The numbers they ended up with were:

• 125 days to harvest.
• That is 127 kg per hour per hectare, or 12.7 gramms per hour per square meter.
• Dry mass of beet is 15% hence 1.9 grams per square meters per hour.
• 45% of that is carbon which is 0.86.
• Carbon is 27% of mass of CO2 (12/44), since one cubic meter of air weighs 1.22 kg and that is 0.117 grams of carbon.

At this point they assumed that a square meter of sugar beet should "pump" 7.37 cubic meters of air through their leaves in order to produce this kind of harvest.

Where is the error (or more than one)?

• Welcome to Biology.SE. Please take the tour and consult the help center starting with How to Ask. In particular, this is a site for clear, focused, well-researched biological questions — it is not a site for debunking crackpot "theories". Among other things, air is not "consumed" by plants (or animals) — you seem to be talking about carbon dioxide? Most importantly show us that you have tried to answer this yourself and how — start by providing references (to reliable sources) for your numbers. This is not simply an answer site, but instead a site that promotes self-learning with some expert help. Commented Dec 31, 2021 at 20:49
• Oh my gosh... I would just totally file that person's belief under "useless to bother arguing with". My own father believed in spontaneous generation. I never argued with him about it. (He was not highly educated, and it would have seemed I was lording my education over him.) Pick your battles to preserve your sanity. Commented Jan 1, 2022 at 3:23
• @tyersome, I would honestly prefer if you've answered this question instead. I've participated on se before and know the drill. Regarding the question I've checked his numbers and tried to calculate amount of carbon plant is supposed to generate myself. The thing is resulting numbers ended up close to his results, and I was unable to find an obvious error in calculations. Which means I'm lacking domain knowledge and that's why I asked it here. It is not debunking. It is looking for a missing knowledge. His conclusion is wrong, but I can't tell why. Hence I ask. Commented Jan 1, 2022 at 8:25
• @anongoodnurse I asked because I'm unable to locate the error in their logic by myself. I don't care about battles, but I'd like to know what the error is. Commented Jan 1, 2022 at 8:27

Taking it slowly;

192 tonnes per hectare is 0.0192 tonnes per square metre (div 10,000)

19.2 kg per square metre over the year

0.1536 kg per day per square metre (div 125 days)

153.6 grams per day per square metre

6.4 grams per hour per square metre. (Div 24)

0.96 grams of dry matter per hour per square metre (x 0.15)

0.432 grams of carbon per ... ( x 0.45)

Derived from 1.584 grams of CO2 (div 12/44)

Using CO2 level of 410 ppm, A cubic metre of air weighing 1.22 kg contains 0.7588 grams of CO2

The averages work out to:

the square metre of beet, per hour uses the CO2 from 2.08 cubic metres of air. (1.584 / 0.7588)

The enzyme RuBisCO captures this CO2.

The amount people breathe isn’t strictly relevant. But....

A common claim is that sedentary people exhale about 1.1 kg of CO2 per day. That’s enough to supply 28 square metres of these beets. (1100/(1.584 x 24))

This sort of maths is sometimes done for hypothetical “how much do I have to grow in my spacecraft” questions

• Thank you very much. Few minor details, however: The original poster I ran into also took day time into account (different from spacecraft, as spacecraft can have continuous light).... and I recall that sugar beet is 20% sugar and 5% pulp. Does the dry matter calculation take that into account? Commented Jan 1, 2022 at 15:28
• I haven’t investigated the dry matter calculation; but I feel that carbon content of dry matter will be fairly constant, by a factor of two anyway. That’s a huge crop - but I regard it as referring to whole plant. Carbon content in sugar similar to carbon content in cellulose or lignin. Commented Jan 2, 2022 at 0:53