1. Round webs have sticky spiral threads and non-sticky radial threads
Round webs have threads that radiate from the center to the outside (radial threads) and threads wound in a spiral (spiral threads). Only the spiral threads are sticky; the radial threads are not [1][2]. If you look closely at the sticky threads, you see small balls of sticky fluid (glue droplets) lined up at regular intervals like beads on a string. Insects stick to these glue droplets [1]. The spacing between droplets is reported to be about 0.1 to 0.3 mm, and their size is about 0.03 to 0.04 mm. These measurements vary depending on the spider species and humidity [4].
When moving across a completed web, the 2 spider species that were studied tended to move along non-sticky threads, such as the radial ones [6]. This is the well-known answer. However, this applies only to spiders that build round webs. In Japanese explanations, spider researchers also state that in round webs, only the spiral threads are sticky, and spiders walk along the radial threads [3].
2. Why web-building spiders cannot avoid touching sticky threads
Consider how a spider builds its web. Spiders in the orb-weaver family, which build round webs, stretch threads while pressing against the sticky ones with their back legs. A 2012 paper states that this happens hundreds to thousands of times for a single web [5]. Yet, the spider does not get stuck and unable to move. If the spider only chose non-sticky threads while walking, this building process should not work. The paper pointed out this as a weak point in the "avoiding sticky threads" explanation [5]. If it is safe to touch sticky threads hundreds or thousands of times, perhaps there is something special about the legs themselves. Researchers thought this way.
3. The old theory that spiders coat their legs with oil
In the early 20th century, researchers like Fabre thought that orb-web spiders coated their legs with oil from around their mouth to prevent sticking to their own webs. However, this observation was simple and was not reproduced or quantified [5]. Later, arguments arose that the "oil" theory was a myth. One explanation, from a 1991 paper, stated that spiders mostly avoid sticky threads and move on their tiptoes using fine hairs on their leg tips, so no protective substance is needed [5]. Some Japanese explanations also focus on walking on radial threads and leg tip hairs, stating that oil is supplementary and of low importance [8]. The oil theory was set aside for a while. Then, in 2012, researchers tried an experiment.
4. A 2012 test: washed spider legs stuck more than twice as much
In 2012, Briceño and Eberhard from the University of Costa Rica and the Smithsonian Tropical Research Institute measured the force needed to peel a leg off a sticky thread using legs detached from spiders [5]. When the leg tips were washed with a solvent similar to oil (hexane) or water, the force needed to peel them off became more than twice that of unwashed legs. It is thought that washing removed something from the leg surface, making it stickier [6]. Furthermore, for legs where the hairs were shaved off, the force needed was about 7 times that of normal legs, even without washing. This shows that the hairs have a large effect [6]. There are important notes. The experiment used detached legs, so it does not perfectly represent the movement of a living spider. Also, because washing with water also increased sticking, it cannot be said that "oil is the only reason" [6].
5. Three ways spider legs may avoid sticking to the web
According to a Smithsonian announcement, the 2012 study suggested three mechanisms [7]. First, the branched hairs on the legs reduce the area that touches the web's stickiness. In explanations by spider researchers, if a spider does stick, the glue droplets catch on the branched parts of the hairs [3]. This is similar to the difference between touching candy with your whole palm versus just touching it with your fingertips. However, the hairs are branched and have a shape quite different from fingers. Second, is how the legs are placed and lifted. They move to minimize contact with sticky threads and do not pull on the thread itself [7]. Third, is a chemical coating on the leg surface that weakens sticking. A preliminary analysis found substances similar to oil on legs washed with hexane, but the source of these substances is not known. The old "from the mouth" theory was not confirmed in this study [6].
6. How to observe which threads a spider uses on a round web
If you find a round web, try to distinguish the threads radiating from the center and the spiral threads from a distance. Watch for a while to see which threads the spider mainly places its legs on and how it moves along the threads. Whether the same tendency exists in spider species other than the 2 studied in the research mentioned here is something you can check with your own eyes. Do not break the web or touch the spider. At home, you can draw a round web on paper. Use a ruler to draw 8 straight lines from the center to the outside, then connect them with a spiral line. If you use different colors, the difference between sticky threads (spiral) and non-sticky threads (radiating from center) is clear at a glance. Then, trace the spider's path with a pencil to think about which lines are easier to walk on. The paper by Briceño and Eberhard is in English, but the abstract is short and includes charts. The Smithsonian announcement also introduces the same study.