# What is missing in the conversion of specific impulse from units of seconds to thrust/mass flow rate? [duplicate]

I was trying to get the Specific Impulse of the Saturn V engines, hoping for a value in N/kg/s, as I need to know the mass consumption rate per thrust value. Any and all sources give me the value in seconds: 263s, rather than what I'm looking for. Trying to convert from this unit into N/Kg/s leaves me clueless as I end up at m/s. Now I know dividing velocity by acceleration, g, leaves you with seconds, thus having: $$s = \frac{N}{kg/s} = \frac{kg\times m}{s^2} \times \frac{s}{kg}= \frac{m}{s}$$ To finish with units of s: $$s = \frac{m}{s}\times \frac{s^2}{m}$$ Thus, $$I_{sp}\space\left(\frac{N}{kg/s}\right) = g \times I_{sp}(s)$$

But I can't figure out why you must introduce g into the equation as it doesn't appear during the dimensional analysis. I very well could be missing critical information though which is why I'm here.

Additionally different sources give me different formulas for the Isp itself, some saying it's $$\frac{F}{\dot{m}}\space$$versus$$\space\frac{F*\Delta T}{\dot{m}}.$$ The NASA webpage for $$I_{sp}$$ words the formula as $$\frac{Total-Impulse}{\dot{m}* g}$$, but the final formula shows as $$\frac{F}{\dot{m*g}}$$.

• I feel like this has been addressed here more than once. Anyway, Isp is thrust / flow rate, so all you need is 1/Isp to get flow rate / thrust. Commented Aug 6, 2023 at 11:46
• That link eventually help me understand. The thing I was missing was something from the rocket equation itself which is that Veq = F/MFR. Commented Aug 6, 2023 at 21:12