Guest post by Frank Lansner, civil engineer, biotechnology.
(Note from Anthony – English is not Frank’s primary language, I have made some small adjustments for readability, however they may be a few passages that need clarification. Frank will be happy to clarify in comments)
It is generally accepted that CO2 is lagging temperature in Antarctic graphs. To dig further into this subject therefore might seem a waste of time. But the reality is, that these graphs are still widely used as an argument for the global warming hypothesis. But can the CO2-hypothesis be supported in any way using the data of Antarctic ice cores?
At first glance, the CO2 lagging temperature would mean that it’s the temperature that controls CO2 and not vice versa.
Click for larger image Fig 1. Source: http://www.brighton73.freeserve.co.uk/gw/paleo/400000yrfig.htm
But this is the climate debate, so massive rescue missions have been launched to save the CO2-hypothesis. So explanation for the unfortunate CO2 data is as follows:
First a solar or orbital change induces some minor warming/cooling and then CO2 raises/drops. After this, it’s the CO2 that drives the temperature up/down. Hansen has argued that: The big differences in temperature between ice ages and warm periods is not possible to explain without a CO2 driver.
Very unlike solar theory and all other theories, when it comes to CO2-theory one has to PROVE that it is wrong. So let’s do some digging. The 4-5 major temperature peaks seen on Fig 1. have common properties: First a big rapid temperature increase, and then an almost just as big, but a less rapid temperature fall. To avoid too much noise in data, I summed up all these major temperature peaks into one graph:
Fig 2. This graph of actual data from all major temperature peaks of the Antarctic vostokdata confirms the pattern we saw in fig 1, and now we have a very clear signal as random noise is reduced.
The well known Temperature-CO2 relation with temperature as a driver of CO2 is easily shown:
Fig 3.
Below is a graph where I aim to illustrate CO2 as the driver of temperature:
Fig 4. Except for the well known fact that temperature changes precede CO2 changes, the supposed CO2-driven raise of temperatures works ok before temperature reaches max peak. No, the real problems for the CO2-rescue hypothesis appears when temperature drops again. During almost the entire temperature fall, CO2 only drops slightly. In fact, CO2 stays in the area of maximum CO2 warming effect. So we have temperatures falling all the way down even though CO2 concentrations in these concentrations where supposed to be a very strong upwards driver of temperature.
I write “the area of maximum CO2 warming effect “…
The whole point with CO2 as the important main temperature driver was, that already at small levels of CO2 rise, this should efficiently force temperatures up, see for example around -6 thousand years before present. Already at 215-230 ppm, the CO2 should cause the warming. If no such CO2 effect already at 215-230 ppm, the CO2 cannot be considered the cause of these temperature rises.
So when CO2 concentration is in the area of 250-280 ppm, this should certainly be considered “the area of maximum CO2 warming effect”.
The problems can also be illustrated by comparing situations of equal CO2 concentrations:
Fig 5.
So, for the exact same levels of CO2, it seems we have very different level and trend of temperatures:
Fig 6.
How come a CO2 level of 253 ppm in the B-situation does not lead to rise in temperatures? Even from very low levels? When 253 ppm in the A situation manages to raise temperatures very fast even from a much higher level?
One thing is for sure:
“Other factors than CO2 easily overrules any forcing from CO2. Only this way can the B-situations with high CO2 lead to falling temperatures.”
This is essential, because, the whole idea of placing CO2 in a central role for driving temperatures was: “We cannot explain the big changes in temperature with anything else than CO2”.
But simple fact is: “No matter what rules temperature, CO2 is easily overruled by other effects, and this CO2-argument falls”. So we are left with graphs showing that CO2 follows temperatures, and no arguments that CO2 even so could be the main driver of temperatures.
– Another thing: When examining the graph fig 1, I have not found a single situation where a significant raise of CO2 is accompanied by significant temperature rise- WHEN NOT PRECEDED BY TEMPERATURE RISE. If the CO2 had any effect, I should certainly also work without a preceding temperature rise?! (To check out the graph on fig 1. it is very helpful to magnify)
Does this prove that CO2 does not have any temperature effect at all?
No. For some reason the temperature falls are not as fast as the temperature rises. So although CO2 certainly does not dominate temperature trends then: Could it be that the higher CO2 concentrations actually is lowering the pace of the temperature falls?
This is of course rather hypothetical as many factors have not been considered.
Fig 7.
Well, if CO2 should be reason to such “temperature-fall-slowing-effect”, how big could this effect be? The temperatures falls 1 K / 1000 years slower than they rise.
However, this CO2 explanation of slow falling temperature seems is not supported by the differences in cooling periods, see fig 8.
When CO2 does not cause these big temperature changes, then what is then the reason for the big temperature changes seen in Vostok data? Or: “What is the mechanism behind ice ages???”
This is a question many alarmists asks, and if you can’t answer, then CO2 is the main temperature driver. End of discussion. There are obviously many factors not yet known, so I will just illustrate one hypothetical solution to the mechanism of ice ages among many:
First of all: When a few decades of low sunspot number is accompanied by Dalton minimum and 50 years of missing sunspots is accompanied by the Maunder minimum, what can for example thousands of years of missing sunspots accomplish? We don’t know.
What we saw in the Maunder minimum is NOT all that missing solar activity can achieve, even though some might think so. In a few decades of solar cooling, only the upper layers of the oceans will be affected. But if the cooling goes on for thousands of years, then the whole oceans will become colder and colder. It takes around 1000-1500 years to “mix” and cool the oceans. So for each 1000-1500 years the cooling will take place from a generally colder ocean. Therefore, what we saw in a few decades of maunder minimum is in no way representing the possible extend of ten thousands of years of solar low activity.
It seems that a longer warming period of the earth would result in a slower cooling period afterward due to accumulated heat in ocean and more:
Fig 8.
Again, this fits very well with Vostok data: Longer periods of warmth seems to be accompanied by longer time needed for cooling of earth. The differences in cooling periods does not support that it is CO2 that slows cooling phases. The dive after 230.000 ybp peak shows, that cooling CAN be rapid, and the overall picture is that the cooling rates are governed by the accumulated heat in oceans and more.
Note: In this writing I have used Vostok data as valid data. I believe that Vostok data can be used for qualitative studies of CO2 rising and falling. However, the levels and variability of CO2 in the Vostok data I find to be faulty as explained here:
http://wattsupwiththat.com/2008/12/17/the-co2-temperature-link/
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OT but amazing:
Two billion years ago parts of an African uranium deposit spontaneously underwent nuclear fission. The details of this remarkable phenomenon are just now becoming clear.
By Alex P. Meshik
http://www.sciam.com/article.cfm?id=ancient-nuclear-reactor
barry moore (23:26:51) :
THANK YOU BARRY,
I APPRECIATE YOUR THOUGHTS.
QUESTIONS/COMMENTS IN CAPS BELOW.
THANKS, ALLAN
Allan. An interesting post and it reiterates many points I have been trying to make. One of the responses I had was that grasses do not suffer from the low CO2 as much as other plants I still have to check this out, there is a wealth of research material on the effect of enhanced CO2 on plant life I do not think there is so much on depleted CO2 but I intend to follow it up.
I must disagree with you on the significance of leaf stomata, earlier I posted a reference to a paper on this subject, the correlation between CO2 and leaf stomata from 1950 to 2000 was studied and the proxy is found to be very robust. Unlike the ice core samples which are 1000 year averages in a single sample the leaf stomata are very date specific the biggest problem is dating the sample by carbon dating when dealing with very old fossils. The paper I referenced addressed the time period from 6800 BP to 8000 BP so the carbon dating was quite accurate since the half life of 14C is 5730 years.
STOMATA COMMENTS ARE FROM WIKI (NOT THE BEST SOURCE FOR AGW INFO)
I have already addressed one of your questions which is the ice core samples are proven to be 30 to 50% low so the CO2 never got that low thus no die off of vegetation and animal starvation which is supported by fossil remains.
CAN YOU PLEASE PROVIDE A REFERENCE OR TWO?
I HYPOTHESIZED SIMILAR IN A POST HERE RECENTLY – I QUESTIONED WHETHER CURRENT CO2 LEVELS ARE TRULY HISTORIC HIGHS – MORE LIKELY ANOTHER RESULT OF GRAFTING TOGETHER DISSIMILAR DATASETS (SEE MANN-MADE GLOBAL WARMING).
I think it is established that the CO2 came from the oceans as they warmed up. YES, TEMPERATURE LEADS CO2, EXSOLUTION AND ALL THAT… …BUT NOT ALL CO2 CAME FROM OCEANS, ESPECIALLY IF PLANT LIFE ON EARTH WAS COMPROMISED. SINGLE SEASONAL CO2 VARIATION IS ~20 PPM/YEAR IN THE FAR NORTH, VERSUS ~140 PPM AMPLITUDE FOR AN ENTIRE ICE AGE.
Yes if we had 1000 ppm CO2 we would be living in a much better world. But the Milankovitch cycles will take care things and humanity will freeze in another 10 000 years but that really will not bother us will it. NOTWITHSTANDING OUR FAILURES AS A SPECIES, I SUGGEST THAT THIS WOULD BE AN UNFORTUNATE END TO THE HUMAN EXPERIMENT.
WE MAY HAVE SOME TIME LEFT TO CONSIDER HOW TO COUNTERACT THESE DOMINANT FORCES OF NATURE, ONCE WE GET OVER THIS OBSESSION WITH AGW… 🙂
Just got to post this:
http://science.nasa.gov/headlines/y2006/10mar_stormwarning.htm
with less than 1 year left to Hathaway’s 03/06 prediction of a monster Solar Maximum in 2010, I thought that it would be refreshing to see the thought process before the actual results chilled the waters.
Solar physicist David Hathaway of the National Space Science & Technology Center (NSSTC) explains: “First, remember what sunspots are–tangled knots of magnetism generated by the sun’s inner dynamo. A typical sunspot exists for just a few weeks. Then it decays, leaving behind a ‘corpse’ of weak magnetic fields.”
Gulp! That means that today’s sunspots (while supplies last) are almost stillborn.
So when exactly did we see the last typical sunspot, or as they say on ABC’s Lost, “Where are we?” ???
Ron de Haan (03:48:57) :
That line was immediately followed by “Editor’s Note: This article originally appeared in the October 2005 issue of Scientific American.” The natural reactor was found in 1972, my father like to point out that the reaction products pretty much stayed in place, they didn’t leach out into surrounding areas. That 2005 article is quite good and worth reading.
I see that page has a link to Coal Ash Is More Radioactive than Nuclear Waste. He worked in the control system field producing equipment used in both coal and nuclear plants and was a fan of atomic power. At the time I was in Pittsburgh at CMU where I picked up a strong dislike of coal, coal ash, SO2, NOx, etc.
BTW, the headline on that story is completely bogus and wouldn’t have been used back when Scientific American was a respected magazine. A more accurate statements is at the end, “In fact, the fly ash emitted by a power plant – a by-product from burning coal for electricity – carries into the surrounding environment 100 times more radiation than a nuclear power plant producing the same amount of energy.” The referenced ORNL report, CoalCombustion: Nuclear Resource or Danger? shows that fissionable isotopes in fly ash can release more energy than burning the coal released. (Breeder reactors required for most of that.)
Again, Dad liked that report – if nuclear plants started releasing 100X as much radioactive material as they do now, putting them on par with coal plants, there’d be a huge response aimed at shutting them down.
TonyB,
I have had some questions arising from your graphs but didn’t get a chance to post a comment yesterday. Your follow up post @ur momisugly(06:26:32) with Beck’s comments has more than satisfied my thirst for better understanding of the data.
It is very easy for all of us to query and criticise dry scientific papers; they often have a very narrow context and the scientists themselves are aware of the data strength or limitations. The pressure to publish, and what you can publish are two further considerations. Published data is the tip of the iceberg of knowledge.
Robert Bateman (04:35:33) :
A more technical report that you’ll like is Hathaway and Wilson’s Geomagnetic activity indicates large amplitude for sunspot cycle 24 that predicts a peak sunspot number of 160 +/- 14. It also references Leif’s prediction of the time (2005) of 75 +/- 6.
Note that while 160 +/- 14 is almost laughable in our current understanding, the understanding of the day made that estimate quite reasonable. As was (and still is) Leif’s prediction. No rancor, no criticism of other predictions or techniques, simply science the way it is supposed to work.
Mary Hinge (02:49:04) :
Therefore, what we saw in a few decades of maunder minimum is in no way representing the possible extend of ten thousands of years of solar low activity.
Ten thousand years of Maunder Minimum Sun would cool the climate system 0.05 degrees.
The downhill world is alive and well within the GCMs… Yup, we’re heading downhill to hell in a handbasket with downhill wheels – Mike Bryant
Pursuing the idea of a DownhillWorld, where everything threatens to go tumbling downhill in avalanches, I suddenly realised why global warming alarmists call the sceptics “Flat-Earthers”. I used to think that it was because the alarmists had an advanced ‘Copernican’ understanding of the universe, while sceptics still clung to a ‘Ptolemaic’ conception of it, complete with epicycles. But now it seems quite clear to me that sceptics live, quite literally, on a flat earth. An earth on which if a tennis ball is dropped onto the ‘flat’ ground, it will bounce a bit, and then come to a stop. But the alarmists live in a world where, if you drop a tennis ball onto the ground, it’ll bounce away, gathering speed and momentum in the process, with possibly fatal consequences for someone in a neighbouring country.
You’ve taken the notion of a DownhillWorld and universalized it to encompass a whole mentality shared by almost an entire generation. And most likely that’s right It’s one in which what seem little problems to flat-earthers (CO2 in the atmosphere) become big problems, and what seems like big problems (providing the energy to power industry, and to warm homes) become little problems. In DownhillWorld, everyone worries about one sort of imminent runaway catastrophe or other – global warming, epidemics, forest fires -, and they’re not too bothered about energy supplies. That can be done with a few windmills and solar panels. And that’s because in DownhillWorld, there’s a superabundance of energy. There’s far too much of the darn stuff. It’s the poor, toiling flat-earthers, who use up precious (hard to come by) energy plodding around on a flat earth, and who worry about where to get fuel to power their cars and food to fill their stomachs.
Alarmists and sceptics inhabit quite different conceptual worlds, and have different priorities as a consequence. This extends far beyond the localised matter of global warming. It touches upon more or less everything – economics, ethics, and so on. It’s becoming a matter of urgency to show which conceptual scheme is the more realistic, the more in accordance with facts.
There’s nothing new about this. Human history is always like this, with one grand conceptual scheme of things competing with another. And we always seem to be going downhill to hell in a handcart.
Well, I had troubles with my Internet link, couldn’t come in yesterday, but 305 responses in just two days must be a record!
To begin with: Frank made a very clear representation of the ice core – CO2 response. I only can ad two relevant graphics to that.
First about the lag and response of CO2: In theory, it is possible that CO2 has an effect on temperature, as in most cases there is a huge overlap between temperature increase/decrease and CO2 increase/decrease. But there is one exception: the end of the Eemian (the last warm(er) period before the current one). The temperature decreased slowly, while CO2 levels remained high for the full period. At the moment that temperatures were at minimum (and ice sheets at maximum), CO2 levels started to drop with about 40 ppmv. This drop should cause a drop of about 0.4°C (if we take into account the GCM feedbacks, causing 3°C/2xCO2), but not seen at all in the ice core.
See: http://www.ferdinand-engelbeen.be/klimaat/eemian.html
Thus anyway, the influence of CO2 is (much) smaller than what the models predict.
Contrary to what Alan MacRae believes, it is perfectly possible that two variables show a positive feedback on each other, despite a lag of one of them. There shouldn’t be a runaway effect, as long as the combined fortifying effect is smaller than 1. In the case of temperature and CO2, if CO2 has a strong feedback effect, that should be noticed in the detailed Epica Dome C ice core record, but again it is not visible:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/epica5.gif
With thanks to André van den Berg, who made the graph.
Again, we see a clear (lagged) response of CO2 after temperature, and no response at all from temperature on CO2, while that should be visible, if CO2 is responsible for 40% of the increase in temperature as Hansen says.
Hansen bases his CO2 influence estimate on the glacial – interglacial transitions, as that CO2 is “needed” to reinforce the initial warming, but a different estimate of e.g. ice/vegetation albedo changes and/or cloud cover (nobody knows anything about that from ancient times) will do the job as effectively…
Further there is a remarkaby linear correlation between CO2 and temperature over the full 420,000 years:
http://www.ferdinand-engelbeen.be/klimaat/klim_img/Vostok_trends.gif
This in fact refutes that there is migration of CO2 in the (deepest) ice cores. If that happened, the ratio between CO2 and temperature (about 8 ppmv/°C) wouldn’t be constant over the 4 cycles, but decreasing in time.
Most of the objections made by Jaworowski and others against the low CO2 levels in ice cores were refuted already over 10 years ago by Etheridge. More comment here:
http://www.ferdinand-engelbeen.be/klimaat/jaworowski.html
Last but not least, the Vostok (and all other) ice core(s) are in contradiction with Frank’s take on the current influence of temperature on CO2 levels in the other thread: his formula says that the increase of CO2 per year is about 3.5 times the temperature difference against a base line. For ice age – interglacial transitions that is only 0.0016 times the temperature difference. In my opinion, temperature has a fast reponse from CO2 on short term (3 ppmv/°C, NOT per year!), from vegetation and ocean surface, while the long-term response (of 8 ppmv/°C) includes deep ocean exchanges and changes in land/ice area…
The problem is that because Frank bases his formula on a high short-term correlation between temperature and CO2 increase (which is right), but uses that including a less good (and spurious) correlation between CO2 increase over the past 50 years and temperature… More on that at the other thread…
“We now know he was wrong then and I’m afraid he is once again very wrong here.”
Yes, I was wrong too. Call me crazy but your arguments for your own view did not impart the light of understanding to me. Yes you ‘know’ but how, because the BOM is more trustworthy than NOAA?
How’s the weather?
“Myself, I’ll bet on the Physics over the “natural trends”.”
But the physics indicates that human produced CO2 is a minor effect. You have to add complex speculation to get to the point where some other factor actually causes significant warming.
George E. Smith (30/01):
Well CO2 is not a problem at the south pole, they measure CO2 in air at some lower level (-4 ppmv), compared to MLO, but that is mainly due to the slow exchange between the NH and SH.
Further, the Vostok ice “temperature” has nothing to do with the local temperature: ice is formed from snow that is formed from water vapor that was evaporated far away. For Vostok, that is supposed to be from a large area of the SH oceans. Colder oceans evaporate less 18Owater and less D2O (deuterium oxide or “heavy water”), relative to “normal” water. Both ratio’s are used to estimate the SH temperatures at the time of ice deposit…
Alan some of the references you requested
Theses can be found in the ICECAP.us library
http://icecap.us/index.php/go/climate-library
http://homepage.ntlworld.com/jdrake/Questioning_Climate/userfiles/Ice-core_corrections_report_1.pdf
http://folk.uio.no/tomvs/esef/np-m-119.pdf
http://www.warwickhughes.com/icecore/
There is a lot of interesting reading in this library.
The stomata paper I only have as a pdf however one of the authors has a lot of interesting information re stomata see
http://www.bio.uu.nl/~palaeo/people/Rike/index.html
actually I have just found the paper I was referring to here
http://www.pnas.org/content/99/19/12011.full.pdf
In general the stomata research totally destroys the ice core data and thereby the entire IPCC assessment reports.
Ferdinand
“Most of the objections made by Jaworowski and others against the low CO2 levels in ice cores were refuted already over 10 years ago by Etheridge. More comment here:”
So who has refuted the stomata data which agrees with Jaworowski. Where are your “testable results” as Einstein would say to back up the critique. The ice core data appears to stand in splendid isolation with no backing from any other methodology.
Idlex,
I think you have the outline for a book there. I’m not sure what type of book it might be though. Would it be fiction or non-fiction? Would it be a book on psychology? Perhaps it could be a children’s book complete with colorful pictures of DownhillWorld, or maybe a thought provoking short story. Could a youtube video be produced which might flesh out the concept even further, or has it already found it’s proper place here as only a few off topic comments in a popular blog?
I hope not…
Mike Bryant
PS Maybe a whimsical essay that Anthony could post under the “fun” category…
Lief
“Ten thousand years of Maunder Minimum Sun would cool the climate system 0.05 degrees.”
I hate to burst your little fantasy bubble but the only instrumental record we have from that period comes from central England and is the oldest thermometer data on record it shows a drop of approximately 1.5 deg C in annual average temperature over that period of time.
Barry Moore:
If you mean by “proven” the work of Jaworowski, better think twice. Jaworowski has a lot of objections which give “possible” problems, but most of them the opposite of what he says (cracks and clathrates in the ice lead to too high levels of CO2, not too low) and most of what he says is refuted by the work of Etheridge (three ice cores, different drilling methods, firn and ice core measurements,…).
Further, even if the “global” CO2 was (too) low in the ice core to sustain vegetation, vegetation itself produces local CO2, which increases average CO2 levels in the lower atmosphere over land with many tens of ppmv’s. Reason why many of the historical CO2 measurements series from Beck are positively biased and show huge variability and stomata data suffer of the same problems.
barry moore says:
Your claim in no way contradicts Leif’s point (and I should get points for correctly spelling Leif’s name!).
His point is that the reduction in TSI is so small that it could only account for 0.05 degrees of the drop in average temperature and that there must be some other mechanism operating, something to do with the storage and transfer of energy in the hydrosphere and atmosphere, perhaps.
nobwainer says:
We’re talking past each other. What you are talking about is the difference in incoming solar radiation between one part of the year and another. This is indeed important in causing the ice sheets to grow or shrink. However, integrated over the yearly cycle, the amount of solar radiation reaching the earth is very nearly unchanged as the eccentricity of the orbit changes (or, for that matter, the tilt of the axis changes in magnitude or precesses)…Hence, there is very little radiative forcing due directly to this change.
Ferdinand Englesteen says:
But this is, I believe, exactly the period that the link that I gave above deal with, repeated here for your convenience: http://www.nature.com/nature/journal/v412/n6846/full/412523a0.html I believe that their corrected temperature no longer shows this behavior…and the two are in much better accord.
Ric:
“The use of geomagnetic activity as a predictor for future solar activity seems counter-intuitive. The Sun is the source of the solar wind disturbances that drive geomag-netic activity and thus it would seem that solar activity should predict geomagnetic activ-ity, not the other way around.- Hathaway”
Then why do it? Why if you know that the Solar Wind distrubances drive your indicator would you want to stick the cart out in front of the horse?
And all this CO2 forcing of climate is sticking the cart out in front of the team, likewise.
We are probably going to end up with a roundabout scheme of the Sun vs the Galaxy in determining Space Weather that in turn drives our Climate on Earth.
If anything, 400 yrs of astronomical discovery had repeatedly drove home the point of just how insignificant man standing on an overshadowed planet is.
Astronomical observations & measuring show 3 planets and a moon undergoing global warming, and it cannot be CO2 forcing due to burning fossil fuels by man.
Now, we got this dark ages mindset trying to bury the observations that keep the fear yoke off of our necks.
That is why I posted Hathaway’s press release, because the man should have bowed out when he knew he was wrong.
Nature hath a way, but it’s not Hathaways thinking.
barry moore (09:33:48) :
“Ten thousand years of Maunder Minimum Sun would cool the climate system 0.05 degrees.”
I hate to burst your little fantasy bubble but the only instrumental record we have from that period comes from central England and is the oldest thermometer data on record it shows a drop of approximately 1.5 deg C in annual average temperature over that period of time.
And what has that to do with the Sun?
Over such long intervals of time, the Total Solar Irradiance is the determining factor [we do not take orbital changes into account for this] [if you disagree, show which other factor is ‘it’ and how much temperature difference that makes]. During the Maunder Minimum TSI was 0.5 W/m2 smaller than today [averaged over a solar cycle] [if you disagree, show how much smaller it was]. 0.5 W/m2 is 0.037% of the average TSI of 1361, so the temperature difference is 1/4 of that [Stefan-Boltzmann’s law: S = aT^4], i.e. 0.009% of 300K or 0.03 degrees, which I conservatively rounded up to 0.05 degrees.
Mr. Lasner cannot specify which AGW theories the Vostok data refutes. The Vostok data is relevant to geologic ages long before humans had any affect on CO2 levels.
I have seen many blogs like “AGW is phony because CO2 lags temperature” and articles like this encourage such fallacious statements.
Eric Anderson (10:22:33) :
MattN (13:43:25) (responding to Eric):
Mike McMillan (16:06:06) (responding to Matt):
Sean Houlihane (05:02:43) (responding to Mike):
Matt, and Sean, you are both wrong in your interpretations of the behavior of springs.
Matt, you are wrong in saying “Except that is not true” because your second sentence is completely consistent with Eric’s statement. Thus it’s obvious that you didn’t understand it. What do you think “another 300 lbs” means? It means 600 lbs for two inches, then 900 lbs for three, etc. Eric was using the correct term, force, in his original sentence because weight in pounds is a measure of force (mass x acceleration). It does take greater weight (force) to move the spring an equvalent distance as you compress more and more.
If the spring took the same amount of force to move the equivalent distance as it was compressed more and more then it would completely collapse once this force was met or exceeded.
Sean, I think you’ve confirmed your understanding of both physics and math. The math in the Wikipedia article you linked to actually confirms Mike’s claim. In order to compress a 300 lb/in spring from it’s resting state by one inch requires a 300 lb force, by two inches requires a 600 lb force, by three inches requires a 600 lb force, etc. Likewise the spring would have only compressed by half an inch if a force of 150 lbs was applied.
So the response of the spring to a linear increase in force is a linear decrease in length.
What Eric got wrong was thinking that the force/length relationship was “logarithmic”. It’s not.
The work/length ratio is however logarithmic. The work required to move that spring 1 inch is 150 pound inches, 2 inches is 600 pound inches, 3 inches is 1350 pound inches, 4 inches is 2400, etc.
The formula being ((300 lbs/inch) * (n inches^2)) /2 = work in lb inches.
So perhaps Eric was thinking of the amount of work required to compress a spring. I don’t however think even work on a spring is a good analogy because most people won’t get it.