A supercharging arrangement for an internal combustion engine comprising: a supercharger having a rotational drive input; a transmission having a rotational drive input to receive drive from the internal combustion engine, and a rotational drive output connected to the input of the supercharger, wherein the transmission includes a variator (Rv) operatively connected between the rotational drive input and the rotational drive output of the transmission, which variator (Rv) has an output that is driven at an operating ratio from an input; wherein the variator (Rv) is of the rolling race type and incorporates at least one rolling element clamped between two races (10, 14), and wherein the variator (Rv) includes (i) an input surface and an output surface, the input and output surfaces being coaxially mounted for rotation about a variator axis, and a toroidal cavity being defined between the input and output surfaces, and (ii) a plurality of rolling elements (20, 22) disposed between and being in driving engagement with the input and the output surfaces at respective contact regions, each rolling element being mounted on a carriage assembly (24, 26) for rotation about a rolling axis, each rolling element being free to pivot about a tilt axis, the tilt axis passing through the rolling element perpendicular to the rolling axis, and intersecting the rolling axis at a roller centre, whereby a change in the tilt angle causes a change in the operating ratio of the variator being the ratio of rotational speeds of the input and output surfaces; a control means for adjusting one or both of the operating ratio and a rate of change of the operating ratio of the variator (Rv); and a control system that operates to cause the engine to adopt a target operating point that is indicated by a state of an input to the control system, the control system being operative to set the operating ratio of the variator (Rv) via the control means, characterized in that to set the operating ratio of the variator (Rv), the control system is operative to generate a supercharger control variable request based on the input, to calculate an air pressure at an outlet of the supercharger, to generate a supercharger air pressure request in response to the calculation, to calculate a mass airflow to achieve the supercharger air pressure request at a current speed (ω c) of the internal combustion engine, to determine a speed of the supercharger to achieve the mass airflow based on a supercharger compressor map, to generate a supercharger speed request in response to that determination, to determine a target variator ratio derived from the ratio of rotational speeds of the input and output surfaces in response to the generation of the supercharger speed request and to modify the target variator ratio to determine a modified target variator ratio. a supercharger having a rotational drive input; a transmission having a rotational drive input to receive drive from the internal combustion engine, and a rotational drive output connected to the input of the supercharger, wherein the transmission includes a variator (Rv) operatively connected between the rotational drive input and the rotational drive output of the transmission, which variator (Rv) has an output that is driven at an operating ratio from an input; wherein the variator (Rv) is of the rolling race type and incorporates at least one rolling element clamped between two races (10, 14), and wherein the variator (Rv) includes (i) an input surface and an output surface, the input and output surfaces being coaxially mounted for rotation about a variator axis, and a toroidal cavity being defined between the input and output surfaces, and (ii) a plurality of rolling elements (20, 22) disposed between and being in driving engagement with the input and the output surfaces at respective contact regions, each rolling element being mounted on a carriage assembly (24, 26) for rotation about a rolling axis, each rolling element being free to pivot about a tilt axis, the tilt axis passing through the rolling element perpendicular to the rolling axis, and intersecting the rolling axis at a roller centre, whereby a change in the tilt angle causes a change in the operating ratio of the variator being the ratio of rotational speeds of the input and output surfaces; a control means for adjusting one or both of the operating ratio and a rate of change of the operating ratio of the variator (Rv); and a control system that operates to cause the engine to adopt a target operating point that is indicated by a state of an input to the control system, the control system being operative to set the operating ratio of the variator (Rv) via the control means, characterized in that to set the operating ratio of the variator (Rv), the control system is operative to generate a supercharger control variable request based on the input, to calculate an air pressure at an outlet of the supercharger, to generate a supercharger air pressure request in response to the calculation, to calculate a mass airflow to achieve the supercharger air pressure request at a current speed (ω c) of the internal combustion engine, to determine a speed of the supercharger to achieve the mass airflow based on a supercharger compressor map, to generate a supercharger speed request in response to that determination, to determine a target variator ratio derived from the ratio of rotational speeds of the input and output surfaces in response to the generation of the supercharger speed request and to modify the target variator ratio to determine a modified target variator ratio.