#!/usr/bin/python -u # -*- coding: latin-1 -*- # # 1RM calculations / Comparing Reps+Weights in Z3 # # Calculation of 1RM for weight training and age adjustment of weights. # See below for sources. # # Example: # We want to know how much a session of 6 reps of 87kg corresponds to # a session of 12 reps. Answer: # # OneRM : 101.03kg age adjusted: 152.96kg # Weight1: 87.00kg age adjusted: 131.72kg # Weight2: 70.16kg age adjusted: 106.22kg # # I.e. a session of 6 x 87kg corresponds to a session with 12 x 70.16kg, # with an 1RM of 101.03kg: this is the value that binds the two sessions # (weights x reps) to each other. # # Also we see the age adjusted weights for Weight1, Weight2, and 1RM. # For a 60 yo man this corresponds to weight x 1.514. # # We can also study - since this is a CP model - how much one have to # lift in order to have a 1RM of 100kg for 6 reps and 12 reps, respectively: # # OneRM : 100.00kg age adjusted: 151.40kg # Weight1: 86.11kg age adjusted: 130.37kg # Weight2: 69.44kg age adjusted: 105.14kg # # [I've have been there for both 6 and 12 reps. # My best so far: # - 12 x 72kg -> 1RM of 103.68kg (age adjusted: 156.97kg) # - 4 x 92kg -> 1RM of 101.03kg (age adjusted 152.96kg) # - 6 x 87kg -> 1RM of 101.03kg (== 4 x 92kg) # ] # # Note: This don't give the same results as http://strengthlevel.com/ : # - Weight*Reps don't give the same OneRM, this model has higher values. # Though brzycki's seems to be nearer than epley's. # - Age adjustments are higher in this model. # # Sources: # # Calculations of 1 RM based on nRM; # The formulas is from Maud & Foster "Physiological Assessments of" # " Human Fitneess" (2 nd ed), page 140. # # (I assume kg in the formulas, but not sure if that' s correct or if it would matter.) # # Also see: https://en.wikipedia.org/wiki/One - repetition_maximum ; # # The age coefficient (1.514 for age 60) is e.g from Meltzer - Faber Age coeffcients: # http://www.mastersweightlifting.org/forms/meltzer.htm # # also: # http://dinosaurtraining.blogspot.se/2016/12/the-difference-between-age-30-and-age-60.html # # Age coefficients: http://www.mastersweightlifting.org/forms/meltzer.htm # # coeffs = { # {30, 1}, {31, 1.016}, {32, 1.031}, {33, 1.046}, {34, 1.059}, # {35, 1.072}, {36, 1.083}, {37, 1.096}, {38, 1.109}, {39, 1.122}, # {40, 1.135}, {41, 1.149}, {42, 1.162}, {43, 1.176}, {44, 1.189}, # {45, 1.203}, {46, 1.218}, {47, 1.233}, {48, 1.248}, {49, 1.263}, # {50, 1.279}, {51, 1.297}, {52, 1.316}, {53, 1.338}, {54, 1.361}, # {55, 1.385}, {56, 1.411}, {57, 1.437}, {58, 1.462}, {59, 1.488}, # {60, 1.514}, {61, 1.541}, {62, 1.568}, {63, 1.598}, {64, 1.629}, # {65, 1.663}, {66, 1.699}, {67, 1.738}, {68, 1.779}, {69, 1.823}, # {70, 1.867}, {71, 1.91}, {72, 1.953}, {73, 2.004}, {74, 2.06}, # {75, 2.117}, {76, 2.181}, {77, 2.255}, {78, 2.336}, {79, 2.419}, # {80, 2.540}, {81, 2.597}, {82, 2.702}, {83, 2.831}, {84, 2.981}, # {85, 3.153}, {86, 3.352}, {87, 3.58}, {88, 3.843}, {89, 4.145}, # {90, 4.493}}; # # Strangely brzycki's formula yield a lower 1Rm than 10RM! # Changed to Wikipedia's version: # brzycki[weight_, reps_] := # weight * (36./(37 - reps));(* weight/1.0278 - 0.0278*reps*) # # epley[weight_, reps_] := 0.033*weight *reps + weight; # epley2[weight_, reps_] := weight (1 + reps/30.); # oconner[weight_, reps_] := weight*(1 + 0.025*reps); # lombardi[weight_, reps_] := weight * reps^0.10; # mcglothin[weight_, reps_] := 100*weight/(101.3 - 2.67123*reps); # wathan[weight_, reps_] := 100*weight/(48.8 + 53.8 Exp[-0.075 reps]); # # # This Z3 model was written by Hakan Kjellerstrand (hakank@gmail.com) # See also my Z3 page: http://hakank.org/z3/ # from z3_utils_hakank import * # # calculate the OneRM | weights | reps according to the oneRM formula. # # Note: age must be a fixed integer. # def oneRM(age,weight1In=None, reps1In=None, weight2In=None, reps2In=None, OneRMIn=None): sol = SolverFor("QF_NIA") # sol = Solver() # Age coefficients, starts at 30 years old age_coeffs = [ 1 , 1.016, 1.031, 1.046, 1.059, 1.072, 1.083, 1.096, 1.109, 1.122, 1.135, 1.149, 1.162, 1.176, 1.189, 1.203, 1.218, 1.233, 1.248, 1.263, 1.279, 1.297, 1.316, 1.338, 1.361, 1.385, 1.411, 1.437, 1.462, 1.488, 1.514, 1.541, 1.568, 1.598, 1.629, 1.663, 1.699, 1.738, 1.779, 1.823, 1.867, 1.910, 1.953, 2.004, 2.060, 2.117, 2.181, 2.255, 2.336, 2.419, 2.540, 2.597, 2.702, 2.831, 2.981, 3.153, 3.352, 3.580, 3.843, 4.145, 4.493 ] # variables age_coeff = 1.0 * age_coeffs[age - 30] weight1 = Real("weight1") if weight1In != None: sol.add(weight1 == weight1In) sol.add(weight1 >= 0, weight1 <= 500) weight2 = Real("weight2") if weight2In != None: sol.add(weight2 == weight2In) sol.add(weight2 >= 0, weight2 <= 500) reps1 = Int("reps1") if reps1In != None: sol.add(reps1 == reps1In) sol.add(reps1 >= 1, reps1 <= 30) reps2 = Int("reps2") if reps2In != None: sol.add(reps2 == reps2In) sol.add(reps2 >= 1, reps2 <= 30) OneRM = Real("oneRM") if OneRMIn != None: sol.add(OneRM == OneRMIn) sol.add(OneRM >= 1) weight1Age = Real("weight1Age") # weight1 age adjusted weight2Age = Real("weight2Age") # weight2 age adjusted OneRMAge = Real("OneRMAge") # OneRM age adjusted # constraints # epley's formula for 1RM given weight and reps # sol.add(OneRM == weight1*(1 + reps1/30.0)) # Don't work in all cases # sol.add(OneRM == weight2*(1 + reps2/30.0)) sol.add(reps1*weight1 == 30 * (OneRM - weight1)) # this works sol.add(reps2*weight2 == 30 * (OneRM - weight2)) # brzycki's formula: slightly lower than epley's # But it don't work in all cases... # sol.add(OneRM == weight1 * (36/(37 - reps1))) # Original formula # sol.add(OneRM == weight2 * (36/(37 - reps2))) # sol.add(reps1 == (37*OneRM - 36*weight1)/OneRM) # Better, but don't always work # sol.add(reps2 == (37*OneRM - 36*weight2)/OneRM) sol.add(weight1Age == weight1 * age_coeff) sol.add(weight2Age == weight2 * age_coeff) sol.add(OneRMAge == OneRM * age_coeff) # print sol print(sol.check()) num_solutions = 0 while sol.check() == sat: num_solutions += 1 mod = sol.model() # print mod print("OneRM: %6.6skg (age adj.: %6.6skg)" % (mod.eval(OneRM).as_decimal(4), mod.eval(OneRMAge).as_decimal(4))) print("Weight1: %6.6skg (age adj.: %6.6skg) Reps: %4.3s" % (mod.eval(weight1).as_decimal(4), mod.eval(weight1Age).as_decimal(4),mod.eval(reps1).as_long())) print("Weight2: %6.6skg (age adj.: %6.6skg) Reps: %4.3s" % (mod.eval(weight2).as_decimal(4), mod.eval(weight2Age).as_decimal(4),mod.eval(reps2).as_long())) print() getDifferentSolution(sol,mod, [OneRM,weight1,weight2,reps1,reps2,weight1Age,weight2Age,OneRMAge]) print() print("num_solutions:", num_solutions) age = 61 weight1 = 100 # None weight2 = None reps1 = 6 reps2 = 12 # None OneRM = None oneRM(age,weight1,reps1,weight2,reps2,OneRM)