Ive been working on my brewing spreadsheet (WIP for about 10 years now) and have been trying to figure out a formula that accounts for as many variables as possible such as mash tun/grain specific heat, grain/mash tun temp and not just a calculator that uses a mash ratio like the Palmer Tw = (.2/r)(T2 - T1) + T2. The reason is that Ill pull a double header and the tun will be about 60+ degrees warmer on the second batch of the day. I did a search and tested the first page of calculators with the following data
Mash Vol: 10.13 gal, 40.5qt 38.32 L
Grain 27lbs 12.25 kg
Mash Ratio 1.5qt/lb
Grain Temp 55°F 12.8 °C
The sites, their input and results are listed below. I tried to standardize the terminology to make things easier to follow and if a formula was listed, I included it too.
http://www.brewheads.com/strike.php
Input: Target Temp, Strike Volume, Grain Mass, Grain Temp, Thermal Loss of Vessel (3)
167.9°F
http://www.rackers.org/calcs.shtml
Input: Mash thickness, Target Temp, Grain Temp
169°F
http://www.tastybrew.com/calculators/infusion.html
Input: Target Temp, Mash Thickness, Grain Temp, Grain Mass
Based on Palmer Initial Infusion Equation:
Strike Water Temperature Tw = (.2/r)(T2 - T1) + T2
166.1
http://www.brew365.com/mash_sparge_water_calculator.php
Input: Mash Volume, Grain Temp, Target Temp, Grain Mass, Mash Thivckness
((((GrainMasslbs*0.05)+MashVolgal)*TargetF) - ((GrainMass*0.05)*GrainTempF))/MashVolgal
166.07
http://www.brewerslair.com/index.php?p=brewhouse&d=calculators&id=cal20&u=eng
Input: Grain Mass, Target Temp, Grain Temp, Mash Vol
170.2
http://www.quaff.org/cyberbrau/StrikeWaterTemp.htm
Input: Grain Mass, Grain Temp, Mash Vol, Target Temp, Mash Tun Thermal Factor (0.12), Mash Tun Mass (33.2lb)
170
http://www.brewblogger.net/index.php?page=tools§ion=strike&action=calculate
Input: Grain Mass, Grain Temp, Mash Vol, Target Temp, Equipment Loss (this just adds to the strike temp)
From Calculations derived from the Brewing Techniques Troubleshooter, Vol. 4, No. 4
http://brewingtechniques.com/library/backissues/issue4.5/miller.html
166.1
http://pint.com.au/calculators/strikewatertemp/
Input: Grain Mass, Grain Temp, Mash Volume, Target Temp
165.5
Strike Temp =
desired mash temp x (litres water + (0.4 x kg malt)) (0.4 x kg malt x malt temp)
litres water
http://texanbrew.com/tbcalcs/index.php
Input: Mash Ratio, Grain Temp, Target Temp, Thermal Loss (3 is default)
168.5
http://www.brewersfriend.com/mash/
Input: Grain Mass, Grain Temp, Mash Ratio, Target Temp
166.1
For the off the shelf software I got the following results:
Beer Smith
Input: Target Temp, Mash Vol, Grain Mass, Grain Temp, Mash Tun Mass (33.2), Mash Ratio, Mash Tun Specific Heat (0.12 cal/gm/C for SS), Grain Specific Heat (0.38 cal/gm/C)
169.5
Promash
Input: Mash Tun Specific Heat (Thermal Mass), Grain Mass, Mash Vol, Mash Ratio, Target Temp, Grain Temp
169.98
It seams to me that what we looking for is the amount of calories require to raise the temp of the grains and the mash tun with a given amount of water as dictated by the mash ratio. The specific heats of the grains, Ive seen 0.367, 0.38 and 0.4 cal/gm/C and for stainless mash tun 0.12 cal/gm/C and water 1.0. When I run the math numbers I get the following.
Grain Temp 12.8 °C
Grain Mass 12.25 kg
Grain Delta 36.7 °C Requires 170.6 cal
MT Temp 12.8 °C
MT Mass 15.06 kg
MT Delta 36.7 °C Requires 66.3 cal
Final Temp 67.2 °C
Mash Vol 38.34L
351.76 Cal required or 9.2°C above target =76.4C= 169.5F
Soooo
((MTw(MTT2-MTT1)(0.12))+(Gw(GT2-GT1)(0.38)))/StrikeVol=Degrees Above Target
Where:
MTw is Mash Tun Weight in kg
MTT2 and GT2 are Target Temp
MTT1 and Gt1 are Mash Tun and Grain initial temps, respectively
StrikeVol is the amount of strike water in L
0.12 is the specific heat for stainless (plastic would be 0.3, Copper 0.092, Aluminum 0.215, Pyrex 0.200)
0.38 is the specific heat for grain