# How even experts get the mix wrong

## Introduction

I've learnt everything I know on this subject from the internet but, if you're serious about pursuing new knowledge and skills, you have to check everything you see or read against what you've learned already, and keep testing yourself.

Even the experts make mistakes, and sometimes these are simple fundamental errors that can throw newcomers right off the track. Here I document instances that have confused me at the time, until I tested myself.

But don't believe me, test yourself.

Note: I have sent comments to the sites I reference here with my suggested "corrections".

## https://johnspeweik.com/2011/10/11/hydrate-lime-vs-lime-putty-mixing/

The author states that the dry lime volume reduces to 75% of the volume as putty, so we need to add 25% more dry lime at the start.

No we don't, we need to add 33% more dry lime at the start.

If a powder reduced to only half the volume as it was mixed with water to become putty, you'd intuitively double the volume of powder at the start wouldn't you? You wouldn't just add another 50%.

Writing down what we know and doing some manipulation:

Ok. The numerical difference in dry lime (1 in 12) is not huge, although we'd complain if every time we bought a dozen eggs we only got eleven. So while we're talking about getting it right we may as well be accurate and at least go away thinking about it correctly.

Out of interest, that would make a 1:3 putty-sand mix a 4:9 dry lime-sand mix, i.e. almost 1:2. However, lime putty optimally needs to mature for several weeks or months and so I would also mature a render that uses dry hydrated lime for a similar period. In the end though it requires far less resources to store the putty until it's needed.

As a footnote, one hydrated lime supplier gives the weight of their bulk lime as 400 to 600 kg per cubic metre. That equates to a specific gravity of 0.4 to 0.6 for their bulk hydrated lime powder. Taking an average of 0.5 and my calculation below suggests that 40 litres (20kg) of that dry hydrated lime would produce 36.5 litres of lime putty (at standard specific gravity of 1.3), or a reduction to 90%.

## https://www.lowimpact.org/infoarticle/lime-plasters-and-renders/

That page contains, as at 8 Dec 2019, the following calculation [in italics]. It appears to conflate two separate objectives.

Calculating coverage

If you consider that a coat of render is around 1cm thick, then one tonne of render will cover 100m², which means 50m² for two coats, and remember that you’ll probably be plastering inside too.

One tonne of render is 3/4 sharp sand and 1/4 lime putty. 1/4 of a tonne is 250kg, which is 10 by 25kg tubs. You may want to mix your own render, in which case you could buy 10 tubs to make a tonne of render, or a tonne bag of putty to make 4 tonnes of render (you can also buy tonne bags of render ready-mixed).

### Objective 1: How much render is needed to cover 100 sq.m ?

Somehow 1 cubic metre of render has been taken to weigh one tonne, which is incorrect. I wouldn’t throw 1 cu.m of render on the back of my 1 tonne flat bed truck (if I had one) unless I wanted to destroy it. It would weigh over 2 tonne.

Best to forget weights and stick to volumes. So the calculation just needs to replace “tonne” with “cu.m”.

I've measured two different sands that I've used and the voids in both was exactly 1/3. I used the saturation method whereby I fill a measure with sand and then add water until it just appears at the top surface. In 300ml of sand I measured 100ml of water.

But then there’s a second more critical error unless I’m mistaken, which is often.

The volume of lime putty required to make 1 cu.m of 3:1 render is not 250 kg nor 250 litres, but 333 litres. This is because the putty is filling the voids in the sand and therefore not adding to the volume of the render produced. To make 1 cu.m of 3:1 render you'll need that much sand, i.e. 1 cu.m and you’ll also need 333 litres of lime putty, i.e. 1/3, not 1/4. Now, a 25kg tub of lime putty is about 19 litres (the specific gravity of lime putty is about 1.35), so you’ll need about 19 tubs, not 10.

That's a very significant error if you're budgeting or ordering for a job.

Then, as was the intention in the example, this 1 cu.m (over 2 tonne) of render will cover 100 sq.m of wall to a depth of 1cm, or 50 sq.m with two coats.

### Objective 2: How big an area will 1 tonne of render cover?

If you just want to make 1 tonne of render then the description is wrong there also. It assumes that sand and lime putty have the same density. They are different. Dry sand has a specific gravity of around 1.6 and wet sand is over 1.9. Lime putty is around 1.33. The ratio of 3:1 for render is a volume ratio and if you mix by weight as in the quoted description you will be over-sizing the lime putty component in the mix.

Mike Wye sells 12kg and 20kg tubs. A 20 kg tub is 15 ltrs so you will need 164/15 = 11 tubs, exactly as the coverage tab on their web page advises for making one tonne (1000kg) of render.

If you want to know what this will cover, the volume of 1 tonne of 3:1 render is equal to the sand volume (remember the lime putty at this ratio only fills the voids), which is 492 ltrs or 0.492 cu.m. Therefore, at 1cm depth, 1 tonne of render will cover about 49 sq.m.

### What are the volume calculations if we have a different void ratio or mix ratio

A different void ratio will effectively change the specific gravity of the sand, which can be easily determined by weighing.

A lower mix ratio, e.g. 2:1, will cause some of the lime to contribute to the volume of the render. A mix ratio greater than 3:1, e.g. 4:1, will leave the render volume the same as the sand volume used, and the set render will be more porous.

Silicon has a specific gravity of 2.33. Checking by accounting for the voids in the sand, if the voids are 1/3 the sand volume then in 3 ltrs of sand we have 1 ltr of air and 2 ltrs of silicon. The specific gravity of sand should therefore be 2.33 * 2/3 = 1.553333 = 1.6 {rounded}.

I've put this into a spreadsheet (see below for updates included in the new version) as a handy way to calculate this stuff. The calculation goes like this:

## https://preservationscience.wordpress.com/2013/09/08/exploring-void-and-pore-space-in-aggregates-2/

This web page does not contain any errors that I can see but is incomplete in describing the starting conditions, e.g. was the sand fully oven-dried? And also incomplete as to how the results should be applied to the actual working mix. Also, a close look at the photos shows excess water at the top, which may be merely surface tension, that I assume has been included as void space, which would be an error.

The article discusses in detail issues with the way porosity is usually measured by artisans. That is, put a measured volume of sand/aggregate into a container and then measure the volume of water needed to just saturate the contents. The volume of water added is the volume of the void space in the sand.

The author found that tamping the sand down and stirring an over saturated sample then pouring off the excess water produced significantly different porosity values and that this process more closely correlates with the mixing process itself. He starts with 200ml of dry sand then adds 100ml of water, stirs the mix and then tamps the container down on the bench before measuring the excess water poured off, which he then subtracts from the 100ml of water added initially. This resulted in a just saturated volume of 175ml total with 55ml of that volume being water (voids).

Suppose we measure out 200ml of dry sand into a container and saturate it using 67ml of water. We then do the compaction test and see the total volume change to 175ml and void space 55ml measured, as in the article. In both cases we calculate the volume of silicon (assuming our sand is almost entirely silicon) and we get: 133ml and 120ml respectively. Something is wrong there because they should be equal and yet there's a 10% difference. There are a few possibilities, assuming our measurements are accurate:

1. there was still some air trapped in the sand in the first test. Sharp sand should tend to trap air more than smooth sand.
2. the sand is not completely dry at the start. Typically sand will contain from 2% to 6% water (by weight) and should be oven-dried before the test. If both tests have 4% water (average) by weight at the start then we have:

Simple subtraction shows the moisture volume in test two to be over 10ml, or 5% of the loose sand volume and 16% of the compacted void space.

The compaction from wetting and mixing will also result in a final mixed volume of render being less than the volume of loose sand going into the mixer, as noted in the article. This shortfall requires a separate ratio to be applied to the initial volume of sand as it is dry loose sand going in. The compaction ratio needs to be applied to the chosen mix ratio, which should be relative to the compacted sand volume, to derive the correct volume of loose sand to load into the mixer. It is possible to calculate the "perfect" mix ratio whereby the lime will exactly fill the voids in the compacted volume of sand.

Reworking the previous methods to incorporate the compaction ratio:

Here's another angle on measuring the porosity of both the loose and compacted sand that avoids trying to determine the water volume taken up by the uncompacted sand:

• fill the measuring cylinder with loose sand and read off the level as S(loose). We know that the volume and weight of the actual solids will remain constant.
• measure W(initial) = S(loose) of water and pour it in, shake, stir and tap as it settles, to compact the solids.
• read off the volume at the top of the water and top of the solids. These are S(compact) and W(cover).

W(compact) = S(compact) + W(initial) - W(cover)

Because the actual solids (Silicon) volume and weight remain constant:

W(loose) = S(loose) + W(compact) - S(compact)

Example from the article:

S(loose) = 200

W(initial) = 100

S(compact) = 175

In this case, the excess water was removed and measured and the remainder then calculated as 55ml. This gives:

W(compact) = 55

W(loose) = S(loose) + W(compact) - S(compact)

= 200 + 55 - 175

= 80

Whereas we need the compacted sand voids volume to determine how much lime could inhabit the mix before adding to the overall volume of render, we need the loose sand voids volume to estimate the volume to throw into the mixer, knowing it will compact in the mixer.

The spreadsheet has been updated to incorporate, and test, these new methods.

## Questions of the meandering kind

### How much lime is in lime putty?

And while we're at it, we should ask what is actually filling the voids? Is it:

• lime putty (calcium hydroxide plus water)
• dry calcium hydroxide (specific gravity of 2.211)
• calcium carbonate (specific gravity of 2.7)

The answer should be that, ultimately, it is the last form, calcium carbonate, but initially it is lime putty that we want filling the voids in the aggregate and making intimate contact with as much internal surface area as possible.

How much calcium carbonate will eventually be in the plaster? For that we need to know how much dry calcium hydroxide is in a litre of lime putty:

Lime putty by volume is mostly water! No wonder it shrinks like crazy.

Note, the quantity VL(solid) in the calculation is the volume of solid calcium hydroxide not including voids. So when making lime putty, use weights for the dry lime and water, which are 0.5477 kg dry lime to 0.7523 kg (litres) of water, or 20:27.5. I've seen a recipe by an artisan on Youtube who used volume proportions 1 part dry hydrated lime to 3/4 part water, which agrees closely with the calculation since hydrated lime in bulk form is roughly 0.4 to 0.6 kg per litre.

According to the calculation above, add one 20kg bag to at least 27.5 litres of water to make 47.5kg (36.5 litres) of lime putty. I say "at least" because adding extra water doesn't hurt and will make it easier to mix and mature, as long as the excess water is removed before you measure out to make the plaster, or mortar etc. The putty will settle out leaving a clear volume of excess limewater at the top.

I haven't ever made lime putty from dry lime because I buy ready made lime putty. It tends to have extra water in it, which I normally put aside to either add a little extra to the mix if needed or to again cover any unused lime putty.

### How much does plaster increase in weight as it carbonates?

Our walls and ceilings gain weight over time.

Three litres of 3:1 sand to lime putty plaster will roughly contain 0.2477 ltrs of calcium hydroxide weighing 0.5476 kg, which will become calcium carbonate weighing 0.6713 kg.

So a ceiling of 3.6m x 3.6m and 25mm thick will increase in weight by 13.36 kg.