The 1/4 wave ground plane antenna seems to be the most common antenna for use on payloads. Its omnidirectional radiation pattern makes it suitable for use on a payload as it will emit equal radio power in the direction of all receivers.
A typical 1/4 wave payload antenna can be constructed from stripping a length of insulation from some 50 ohm coaxial cable (RF174). The copper braid can then be separated into 4 strands and secured in an X formation by either using tape to the bottom of your payload box, straws, or soldering solid core wire to the braid.
You will need:
Measure 170mm from the bare end of the coax and cut the insulation without damaging the braid inside. Gently roll the blade over the cable.
It is important at this point not to cut the braid inside.
The easiest way to do this is to roll the blade around then carefully cut lengthways and remove the insulation in segments.
Make the remaining braid into two stumps and tin :
This is the radiating element. Put this to one side.
Cut two lengths of single core wire about 350mm long. Mark the center point with a pen and then remove about 25mm of insulation from the center.
Again this is easiest by gently rolling the wire on the edge of a blade and then cutting lengthways and removing the insulation.
Using a pen or large nail as a former place the wires around and twist together. Then apply solder to secure them.
From the point where the shield ends measure the radiating element and trim @ 164mm. This value is important.
Repeat with the radials.
Congratulations you've made a light weight 1/4 wave antenna for 433Mhz. It is recommended you secure and straighten the radials and radiating element using straws.
Team Stratodean's payload:
You can trim the straws down but take care not to snip the elements inside. The radials form a ground plane and this can be constructed into the base of the payload. The radiating element should face downwards. The length of the coax from the SMA plug to the start of the antenna isn't important though it is suggested it's kept as short as possible.
You don't need a coax with an SMA plug on it you can solder the other end directly to the board.
Some good information about antenna design and propagation can be found at http://www.idc-online.com/technical_references/pdfs/electronic_engineering/Antennas_and_Propagation.pdf