Aké kolesá na MTB?

a ma niekto realnu skusenost ci je naozaj ten hmotnostny rozdiel na kolesach citit ? oplati sa do toho investovat? mam ponuku na novatec par 1700g tusim flow trail. len sirka rafika je len 20mm co sa mi na bezdusu moc nepaci koli nizsiemu tlaku.

I can't believe that people keep arguing that rotating mass climbs slower than non-rotating mass under the same power. When you are working against gravity, mass is mass, it doesn't matter if it rotates or not. The idea that micro-accelerations due to pedal force fluctations make a difference in the overall picture is a strawman. During pedal force fluctuations, accelerations are decelerations cancel out. All that really matters is average power output vs. gravity.

Since Ras11 complained that no math has been offered, I decided to set up a model to simulate the accelerations/decelerations due to pedal fluctuations. The equations and variable values were taken from the Analytic Cycling web page.

Pedaling force: The propulsion force (from pedaling) was modeled as a sinusoidal. Since it is assumed average power is constant, the nomimal drive force will vary inversely with velocity. So, the propulsion force is modeled as:

Fp = (P/V)(1+Sine(2RT))

Fp = Propulsion force (pedaling)
P = Average power
V = Velocity
R = Pedaling revolution rate
T = Time

(Note: The angle in the sine term is double the pedal revolution rate, since there are two power strokes per revolution)

The drag forces on the rider are aerodynamic drag, rolling resistance, and gravity. These three terms together are:

Fd = (1/2)CdRhoAV^2 + MgCrrCosine(S) + MgSin(S)

Fd = drag force
Cd = Coefficient of aerodynamic drag
Rho = Density of air
A = Frontal area
M = total mass of bike and rider
Crr= Coefficient of Rolling Resistance
g = Acceleration of gravity
S = Slope of road

The total force is thus:

F = Fp - Fd

From Newton's second law, the equation of motion is:

dV/dt = F/I

I = Inertia

Because there is both rotating and non-rotating mass, total mass and total inertial will not be the same. Because mass at the periphery of the wheel as twice the inertia as non-rotating weight, the total mass and inertia of a bike are:

M = Ms + Mr
I = Ms + 2Mr

Ms = Static mass

Mr = Rotating mass

The complete equation of motion is thus:

dV/dt = {(P/V)(1+sin(2RT)) - [ (1/2)CdRhoAV^2 + (Ms+Mr)gCrrCosine(S) + (Ms+Mr)gSine(S) ] } / (Ms + 2Mr)

This equation is non-linear, so I solved it numerically with a 4th order Runge-Kutta numerical differentiation.

Borrowing the default values in the Analytic Cycling web page for "Speed given Power" page, the values used are:

P = 250 Watts, Cd = 0.5, Rho = 1.226 Kg/m^3, A = 0.5 m^2, Crr = 0.004, g = 9.806 m/s^2, S = 3% (= 1.718 deg.)

(http://www.analyticcycling.com/ForcesSpeed_Page.html)

For this simulation, the pedal revolution rate was selected as 540 deg/sec. (90 rpm cadence)

To solve this equation, a 4th order Runge-Kutta numerical differentiation was set up using an Excel spread sheet. Step size was selected at 0.01 sec., and the initial Velocity was 1 m/sec. The solution was calculated for 3 cases of equal total mass, but different distributions of static and rotating mass, calculated over a 200 second period, by which time each case had reached steady state. As expected, the velocity oscillated with the pedal strokes. The average, maximum, and minimum velocities during the oscillilations during stead state were:

Case 1:
Ms = 75 kg, Mr = 0 kg (0% rotating mass)
Average Velocity: 7.457831059 m/s
Maximum Velocity: 7.481487113 m/s
Minimum Velocity: 7.434183890 m/s
Speed fluctuation: 0.047303224 m/s

Case 2:
Ms = 70 kg, Mr = 5 kg (5.33% rotating mass)
Average Velocity: 7.457834727 m/s
Maximum Velocity: 7.480016980 m/s
Minimum Velocity: 7.435662980 m/s
Speed fluctuation: 0.044354000 m/s

Case 3:
Ms = 65 kg, Mr = 10 kg (10.67% rotating mass)
Average Velocity: 7.457837584 m/s
Maximum Velocity: 7.478718985 m/s
Minimum Velocity: 7.436967847 m/s
Speed fluctuation: 0.041751139 m/s

These results agree very strongly with the solution on the Analytic Cycling web page, which predicted an average speed with constant power of 7.46 m/s (16.7 mph)

The results show that as expected, the smaller the percentage of rotating mass, the greater the magnitude of the velocity oscillations (which are quite small). But a more interesting result is in the average speed. As the amount of rotating mass decreased, the more the average velocity _decreased_, not increased (at steady stage). This result is actually not unexpected. The drag forces are not constant, but vary with velocity, especially aerodynamic drage (Because aerodynamic drag increases with the square of velocity, power losses are increase out of proportion with speeds - so, for example, aerodynamic losses at 20 mph are 4 times as much as they would be at 10 mph). Because speed fluctuates as the propulsion force oscillations, in the cases of the low rotating mass, the maximum peak speeds reached are higher than for the cases with the high rotating mass. This means that when a lower percentage of rotating mass there will be greater losses during the speed peaks. Because of the total drag losses will be greater over the long run, the greater momentary accelerations with lower rotating mass actually results in a lower average speed.

To see what happens at a steeper slope, which will have a lower speed (and presumably larger speed oscillattions), I ran the model again with a 10% (5.7 deg.) slope. Here are the results:

Case 1:
Ms = 75 kg, Mr = 0 kg (0% rotating mass)
Average Velocity: 3.217606390 m/s
Maximum Velocity: 3.272312291 m/s
Minimum Velocity: 3.162540662 m/s
Speed fluctuation: 0.109771630 m/s

Case 2:
Ms = 70 kg, Mr = 5 kg (5.33% rotating mass)
Average Velocity: 3.217613139 m/s
Maximum Velocity: 3.268918539 m/s
Minimum Velocity: 3.165997726 m/s
Speed fluctuation: 0.102920813 m/s

Case 3:
Ms = 65 kg, Mr = 10 kg (10.67% rotating mass)
Average Velocity: 3.217618914 m/s
Maximum Velocity: 3.265921742 m/s
Minimum Velocity: 3.169047012 m/s
Speed fluctuation: 0.096874730 m/s

This data follows the same pattern as above. The speed oscillations (micro-accelerations) are greater with the lower rotating mass, but the average speed is also slightly lower with lower rotating mass. So next time you want to claim that lower rotating mass allows faster accelerations, remember too that the greater speed fluctuations (due to greater accelerations) will also results in greater energy losses due to drag forces.

But, in reality, the differences in speed fluctions and average speeds are really very small between all these cases. For all practical purposes, when climbing, it is only total mass that matters, not how it is distributed.

Niekto zobral dedkove tabletky

Mam na jednom biku kolesa povodne co maju cca 2,1 kg a casom som dokupil druhe co maju cca 1,75. Rozdiel v akceleracii obrovsky. Ale ked je v strmom vyslape napr. zopar korenov, tak s tymi tazsimi sa cez tu pasaz lepsie prechadza, mensia strata rychlosti, mensi boj. Aspon taky bol moj pocit z toho.

Asi to malo byt vtipne ci nieco take, no zjavne ti tvoje IQ nepostacuje na pochopenie aj vcelku nie zlozitej matematiky

MageZ nieje to len tvoj pocit, presne to je vysledok aj toho vypoctu vyssie

och som myslel ze jednoznacne lahke kolesa - len na aku vahu ist aby sa to casto neservisovalo a ci ma vyznam kupovat cele nove kola za stovky € koli 300-400g.
ale ono - lahke kolesa - lepsia akceleracia, lahsi bike / tazke kolesa - zotrvacnost, odolnost hmm

Osobne by som volil podľa hmotnosti jazdca a terénu v akom najviac jazdíš, aby to aj niečo vydržalo, myslím že nemá význam gramáriť za každú cenu. Ja mám cca 85-90 kg a do nejakých extra ľahkých kolies by som sa nepúšťal, jazdím aj ťažši, technický terén a pre mňa je dôležitejšia odolnosť ako pár ušetrených gramov, samozrejme, je dobré zvoliť vhodný kompromis, čo nebýva vždy jednoduché. Niektoré ľahké kolesá majú napr váhový limit 90 kg, pri takýchto som už mimo

priznam sa ked da niekto prispevok dlhsi ako 5 riadkov necitam to. a toto mi teda prislo hodne uletene. v celku mi je jedno co je tam, lebo ako vidis co napisali chalani da sa to zhrnut do "jednej vety"

Toto je IMHO čiste matematický výpočet, ktorý má ale jednu "malú" chybičku. Funguje pri ideálnom stúpaní na hladkom povrchu a stálej rýchlosti. V teréne v korenistom výjazde nikdy nejdeš konštantnou rýchlosťou a ako sa terén dvíha alebo klesá potrebuješ meniť rýchlosť. Často krát zrýchľuješ, aby si prekonal strmší úsek a vtedy je malá obvodová hmotnosť na nezaplatenie. Ale aj opačne to samozrejme funguje. Kolesá s nižšou obvodovou hmotnosťou zastavíš ľahšie ako rovnako celkovo ťažké kolesá kde je však hmotnosť viac na obvode vďaka ťažším ráfikom alebo plášťom. Ale vzorec odo mňa nečakaj

Lahke kolesa (vybrat podla hmotnosti jazdca) su vzdy vyhoda a ak sa skombinuju s bezdusakmi, dramaticky sa znizi aj valivy odpor. To pociti urcite kazdy, kto ma uz cosi najazdene.

Gusto0 mozno sa ti zda, ze 300-400g je malo, ale pri kolesach je to poznat ovela viac ako na ktoromkolvek inom komponente.

Môj skromný názor zo skúsenosti za posledného pol roka - úspora 835g vďaka iným kolesám a bezdušiam - obrovský rozdiel. Ako hore písali je to nárast dynamiky, lepšia obratnosť a ľahšie narábanie s bajkom aj vo vzduchu.
Na dirt bajku po zmene kolies a ušetrení cca 500g neuveriteľné zrýchlenie a oveľa jednoduchšie narábanie s bicyklom a o časoch na bikroske ani nehovorím. Za mňa palec hore už pri 300-400g úspore (povedzme z 2100g na 1700g).

Samozrejme ze jazdim tie lahsie. Tie povodne tazitka zostali na zimu. Lahsie kolesa urobia obrovsky rozdiel, ale su miestecka, kde ma to prekvapilo, ze to neslo az tak lahko a zamakal som si o dost viac ako som ocakaval. To bolo na 26" biku. 1e za 1g usetreny je este fajn cena.

Keď som písal na jeseň do suncycle k mattovi, tak mi odpísali, že za tých 300 eur sa vedeli priblížiť k 1600 gramom s oba pevnými nábojmi a 28 špicmi (ja vpredu 15mm vzadu RU)... A tie Mavici sa mi zdá, že sa nejak krútia

to zasa bude penez snad sa do 300-350€ zmestim. na mojich 70kg a moje jazdenie vsetkeho druhu bude stacit nieco medzi 1700-1900g.
na novatec mate aky nazor ?

Aky iny, ako ciste matematicky vypocet chces pouzit, ak chces nieco relane vypocitat?


Zial tuto chybicku nema. Ak by si tomu venovala trosku casu zistila by si, ze to je uplne naopak.
Za prve su tieto veliciny ktore popisujes, zapocitane vo vzorci v realne nameranych cislach a jednotkach, ktore si kludne mozes sama menit podla podmienok ktore ta zaujimaju. Konkretne tento vypocet je pocitany v doch roznych stupaniach, s koeficientom odporu povrchu zodpovedajuci asfaltu, a rychlost sa samozrejme meni radikalne so stupanim (co je evidentne na vysledkoch v roznych stupaniach), kedze pre porovnatelnost vysledkov sa pouzila rovnaka sila.
Za druhe je tento vypocet zamerany na zistenie rozdielu v efektivite zrychlovania a zotrvacnosti, pri zachovani rovnakej celkovej vahy, ale s rozdielnym pomerom rotujucej a nerotujucej vahy. Samozrejme to vies vyratat v roznych sklonoch stupania, ale ako sama mozes vidiet, tak zmenou pomeru rotujucej/nerotujucej vahy su rozdiely v efektivite celkom male a to jak pre 3% tak aj pre 15% stupanie.


Ved jasne. Staci zmenit vstupnu hodnotu stupania a vypocitat si to pre akykolvek uhol. Cim je stupanie strmsie a rotujuca vaha nizsia, tym sa viac prejavuje vyhoda pri akceleracii, ale naopak nevyhoda v zotrvacnosti. Tu preto velmi zalezi od stylu jazdy a samozrejme od toho co ti dovoluje teren. Napriklad ak by sme sa bavili o cestaku kde sa snazis niekolko kilomterov do mierneho stupania udrziavat konstantnu rychlost, tak tam by clovek mohol mierne stratit. Ak sa zase budeme bavit o MTB s narazovymi prudkymi stupaniami, kde celovek pomerne casto akceleruje, tak si urcite pomoze.
Rozdiely ale niesu nijak drasticke. Samozrejme to vsetko plati pri zachovani celkovej vahy (bike+clovek), a zmene pomeru rotacnej a nerotacnej vahy. Takze ak si na bike das lahsie kolesa (tj znizis celkovu vahu), polepsis si urcite v akceleracii v strmsom vstupani vdaka mensej rotacnej vahe, ale viac to bude vdaka znizeniu celkovej hmotnosti.


Ano aj toto je logicke, lenze treba tiez uvazovat o akych rozdieloch v hmotnosti sa tu bavime. Treba si uvedomit, ze to co akcelerujeme a tym padom aj to co brzdime, je nasa celkova vaha aj s bikom. A tak vaha kolies (aj ked pripocitame/odpocitame ten efektivny rozdiel pri stupani/klesani) tvori len pomerne velmi malu cast z toho. To by museli byt kila naviac, aby si citila realny rozdiel v brzdnom ucinku. Dnesne brzdy ubrzdia aj raz tak tazkeho cloveka ako si ty, pomerne velmi rychlo, takze nejake dekagramy su smiesny rozdiel.

Dajme tomu ze celkova vaha bike + clovek je 80kg (67+13). Tu potrebujes akcelerovat/brzdit. Dajme tomu ze kolesa z toho maju 4kg. To je teda iba 5% (a tom som dal ako priklad celkom tazitka) z celkovej vahy ktoru akcelerujes/brzdis. Dajme tomu, ze vymenis kolesa za take co maju iba 3kg. Celkova vaha teda klesne na 79kg a z toho su 3kg rovne 3.80%.

Rozdiel vo vahe ktoru musis akcelerovat/brzdit je teda 1.2% a to pri usetreni 1kg. Dovolim si ale tvrdit, ze uspora na vahe je casto krat ovela mensia ako 1kg .. a tak rozdiel byva casto hlboko pod 1%.
A to mi aj nadalej chcete tvrdit, ze pri uspore 300-400g (dajme tomu 0.5% z celkovej vahy) citite neuverilene rozdiely, z ktorych sa tu idete skoro pototo? Fakt vam to stoji za to neuvazovat, ale len rozsirovat subjektivne pocity ako realne fakty? Naozaj ste spolu s lahsimi kolami nepresli rovno aj na bezduse a na ine plaste (mozna radikalna zmena valiveho odporu)??
Naozaj ale naozaj by som chcel vidiet, keby som dal tunajsim fajnsmekrom na 2 totozne biky, kompletne rovnaky set komplet kolies, ale jedny by mali vyssiu vahu o 400g dajme tomu len kvoli pouzitym materialom a ak by nevedeli ze ktore su ktore a sli sa previezt, ci by to vobec zistili To by museli mat 25kg a to percento tym padom viac porast, aby to bolo tak markantne citelne ako to tu mnohi popisuju.