The ability of technology to transmit multi-media is very dependent on compression techniques. In particular, lossy compression has been used in image compression (jpeg), audio compression (mp3) and video compression (mpg) to allow the transmission of audio and video over broadband network connections. Recently, the sense of touch, or haptics, is becoming more important, with its addition in computer games or in cruder applications such as vibrations in a cell phone. As haptic technology improves, the ability to transmit compressed force sensations becomes more critical. Most lossy audio and visual compression techniques rely on the lack of sensitivity in humans to pick up detailed information in certain scenarios. Similarly, limitations in the sensitivity of human touch could be exploited to create haptic models with much less detail and thus requiring smaller bandwidth. The focus of this paper is on the force thresholds of the human haptic system that can be used in a psychophysically motivated lossy haptic (force) compression technique. Most of the research in this field has measured the just noticeable difference (JND) of the human haptic system with a human user in static interaction with a stationary rigid object. In this paper, our focus involves cases where the human user or the object are in relative motion. An example of such an