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1 Improved Spanreed for use in Multiple Reference Frames Author: u/skemp117 Date: Vevishes 1175 I. I NTRODUCTION results than traditional dynamics as fabrial connections aren’t Current spanreeds cannot transmit writing effectively be- effected by time derivatives in non-inertial reference frames. tween two different frames of reference (1). Because of this, Further notation definitions are that s indicates a spanreed, communication between land and ships is rendered impossible. o indicates a reference frame, t is for transmitter, and r is This is because the single conjoiner fabrial on the device does for receiver. Equation (1) shows the standard form for the not distinguish between the desired movement of the writing equation of a spanreed. The full motion of the receiving fabrial hand and the movement of the reference frame. We propose a is the sum of the relative motion of the transmitter in its frame solution to negate the effects of the different reference frames and the motion of the transmitter’s frame. This is not enough. by adding another conjoiner as well as a reverser. Consider the receiving spanreed located on a moving ship, the position vector II. I MPROVED D ESIGN x̄rs = x̄ts/o + x̄to (1) Adding a reverser seems an obvious move. Place one half Adding the reverser between the receiver spanreed and the of the pair on the receiving spanreed and the other half transmitter reference frame would remove the effects of the somewhere in the reference frame of the transmitting spanreed, transmitter reference frame which are inevitably transmitted an ink-well perhaps. While adding this reverser will remove through the primary conjoiner. The motion of the receiving the effects of the transmitter’s reference frame, the receiving spanreed would now be mimicking exactly the handwriting of spanreed would be unable to account for the movement of its the transmitter. That works great if the receiver is stationary. own frame. Figure 1 shows a simplified sketch of the proposed Consider receiving a message on the deck of a ship. Your span- design. reed would mimic perfectly the handwriting of the transmitter; however, your ship would have sailed out from under the receiver while it hovers over the ocean writing away. Thus we need to add another conjoiner between the receiver’s reference frame and the receiver to add the motion of the ship back to the receiver. Equation (2) shows the new terms. The first parenthesized term is the primary conjoiner, the second term is the reverser, and the third term is the secondary conjoiner. x̄rs = (x̄ts/o + x̄to ) + (−x̄to ) + (x̄ro ) = x̄rs/o + x̄ro (2) x̄ts/o + x̄ to − x̄ to + x̄ro = x̄rs/o + x̄ro (3) As you can see in equation (3), the motion of the transmitter Fig. 1. Improved spanreed and ink-well reference frame is cancelled. Matching terms on both sides of the equation shows us that the handwriting of the transmitter, Spanreeds are unique in that they act as a rigid connection x̄ts/o , is successfully transmitted, and the receiver can continue (not dynamic), transmitting position and not velocity, accel- to move in its reference frame as if rigidly connected to it. eration, or force. Conjoined masses act as rigidly connected masses subject to the forces upon them at the time. Although III. C ONCLUSION one could say you need more force to move these conjoined This paper presents a novel method for transmitting infor- masses, it is equally valid to say that a conjoined items mass mation across Roshar without needing to consider reference is increased by the dimension of the connection that binds frames. We hope this will aid the Coalition with the liberation the masses together through the Cosmere thus increasing the of Alethkar and other nations of Roshar. force needed to effect them. As such, in the following equa- tions, x̄ will represent the infinitesimal 3D change in position R EFERENCES composed of orthogonal delta position vectors (x,y,z) for an [1] “Spanreed.” [Online]. Available: infinitesimally small period of time. This yields more accurate https://coppermind.net/wiki/Spanreed