More about current on a wire

 

The image below shows the current on a wire. The curve is the standing wave of current on the wire while the arrow represents the direction of the current. When the arrows point in the same direction the current is in phase and where the arrows point in opposite directions the currents are out of phase . Note on the half wave wire ( figure 2.8 B) there is only one arrow and that indicates the current is in phase. Where there are two half waves (a full wave long wire) the currents in each half wavelength section will be out of phase if the wire is end fed ( Figure 2.8 A) If, however the antenna is center fed (Figure 2.8 C ) currents in each half wave section will be in phase. If a receiving station is broadside to the full wave end fed wire , it will receive equal strength signals from each half wave section but these signals will be out of phase and tend to cancel each other. There fore there will be a null broadside. In the case of a full wave center fed wire, the receiving station will receive in phase signals from the two halfwave sections.  This is how antenna patterns are formed. The areas of maximum radiation are where the current curve peaks. For any straight section of wire the radiation is proportional to the area under the current curve. In directions where the distance from two sections of the antenna is equal and the currents in those section is in phase ( arrows point in the same direction) the radiation will add completely. In directions where the distance is not equal the radiation will not add completely but will partially add up. For example, if radiation from a two halfwave sections is in phase ( like the center fed example) then broadside to that antenna the radiation simply adds. If it adds to up to 1, then moving off broadside by 45 degrees the radiation will be reduced to 1 times the cosine of 45 degrees  or .707. Moving 90 degrees from broadside the radiation will be 1 times the cosine of 90 or zero. There will be a null. If the current in the two sections in not in phase then directly broadside there will be a null and as you move away from being broadside the two signals will start to add and there will be a peak when 45 degrees off broadside. Then at 90 degrees off broadside there will again be a null. This is because directly broadside the radiation starts out of phase and travels equal distances and therefore stays in phase. At the 45 degree angle they travel different distance and at the 45 degree point one of the signals travels just enough farther that it’s phase has shifted 180 degrees so that the signals are back in phase and add totally. Continuing around to 90 degrees from broadside the signals become out of phase again. These relationships involve sine and cosine functions of the angles involved. 

Note that with the single halfwave wire there are two peaks  ( broadside) and two nulls ( off the ends). With the full wave wire there are 4 peaks and 4 nulls. Peaks are at 45 degrees with the wire and the nulls are directly broadside and off the ends. Wires that are two waves long have 8 peaks and 8 nulls. The peaks and nulls are not all equal and the pattern becomes quite complex as the wire length in wavelengths increases from just a single half wave length or full wave length of wire. 

Computers are good at doing complex trigonometric calculations and displaying these complex patterns. One good such program is EZNEC and its author has now made it free to anyone who wishes to uses it. Many years ago there was a limited free version but I purchased the full program and have been using it to model my antennas.